And was Galen's/the Church's authority enough to cement the four humour theory for that long?

A historian of medicine will hopefully help you with an answer. However, as a historian of the middle ages, I'd like to approach the above misconception about science and medicine's relationship to the medieval church, and at the same time question the idea that Renaissance medicine was distinctly innovative. Below is an answer to the question Was there really no human dissection after antiquity and before Andreas Vesalius? which you might find interesting.

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Medieval Popes and the Invention of Autopsy

One of the long-held, and incorrect, beliefs about the middle ages is that anatomy and dissection were forbidden, in particular under Christianity, and especially by the Catholic Church. Usually this is trotted out in defence of the conflict thesis: the argument that religion, and in particular the medieval Catholic Church, was opposed to science and therefore the progress of humanity. When we look at evidence, we actually see that Innocent III ordered the first recorded autopsies since the classic period, paving the way for dissection science. Moreover, we can recognize these first forensic, legal activities as the direct forebears of today's autopsies.

Two deaths and a Pope in 1209

Let's look at the stories of the first two juridical autopsies recorded in history.

Our first anecdote is of a chaplain at the monastery Sancta Trinitatis of Maloleone near Bordeaux, who:

having surprised a criminal in the act of stealing religious articles from the abbey chapel, struck the would-be felon with a heavy farm implement. The thief fled, despite his wounds, but was finally overtaken by parishioners who dispatched him with swords and clubs. The chaplain, fearing that the blow he had struck might have caused the death of the culprit even if the additional injuries had not been inflicted, related his story to the abbot.

The second is of a bishop at Siguenza near Toledo, who:

disturbed by the rowdy behaviour of a number of his parishioners during Mass, ordered his canons to restore order about the altar. As their efforts proved to be insufficient to control the throng, he seized a cane and began to drive back the crowd by prodding some persons, and lightly striking others. The canons joined into this turbulent activity, and during the resulting melee, a young man was struck on the head. ^1

It would seem the young man was not affected by this blow: testimony states he thereafter ate and drank in taverns, he visited public baths, performed field labour. However, clearly something was amiss after this altercation with the bishop for although a month had passed, he was:

advised to submit to an operation upon his injured head, [and] the victim allowed an old, unskilled physician to cut into both his skull and the flesh of his head. Four days after this operation the young man died, and though four physicians testified that the surgical procedure was ineptly performed, thus causing the youth's death, common talk charged the bishop with having fatally injured the young man with a blow from his cane. ^2

We have both of these stories from Regestorum sive epistolarum, a decretal of Pope Innocent III in 1209. Decretals were issuances of judgement on a variety of ecclesiastical matters, ranging from theology to canon law. In these cases of death involving clergy, both matters were submitted to the papacy for judgement and so come to us with the grounds for decision: the testimony of investigating physicians and surgeons.

In the case of the chaplain chasing the thief from his monastery, the matter was a question of establishing the chaplain's guilt according to Canon Law which stated that when several people are involved in a brawl and there is a death, the person who strikes the lethal blow was guilty of the homicide. Innocent III requested the testimony of expert physicians, and after receiving a report of their autopsy, it was declared that the chaplain did not strike the death blow [peritorum judicio medicorum talis percussio assereretur non fuisse lethalis].

The bishop of Siguenza sought to relieve public suspicion of his role in the death of the youth, suspicion which had jeopardized his position, and he appealed to the papacy for intervention. Again, the sworn testimony of surgeons and physicians was sought by Innocent III, and the pontiff upon examining the evidence sided with the testimony of these surgeons and physicians who declared the death a result of the botched surgery, and not the result of the bishop's blow [duo vero chirurgici et unus physicus jurari dixerunt quod non ex percussione sed indiscreta incisione obierat juvenis memoratus].

That Innocent III made central the function of law and legal process resulting in autopsies should not surprise us. Why not?

Origins in Medieval Law and Medicine

The scholastic effect of the medieval Christian Reconquista is a well-worn story by now, but worth restating briefly for its importance to our tale of how a pope came to lead the first recorded autopsies.

In the 11th century the Reconquista had taken scholastic Moslem cities such as Toledo, provoking the contact between Christian and Moslem scholastics, and in particular exposing Christian scholastics to unknown Greek and Roman works (in Arabic) as well as Arabic advancements. These covered science subjects like math, chemistry, physics, medicine, and also, perhaps most famously, Aristotelian philosophy. The path this knowledge followed into western European scholasticism are fairly complex and still being understood, but we can say that while the masters at the new universities of Oxford and Paris took up the massive theological implications of Aristotle’s works, the university cities of modern Northern Italy and Provence (Bologna, Milan, Montpellier) became centers of the resulting legal and medical scholasticism. ^3

By the middle of the 12th century, the university corridor of Bologna-Milan was the center and fount of legal scholasticism and training. It was here that Roman law was rediscovered, assembled, codified, and interpreted in the form that remains the basis of continental European (and other) legal systems today. Both this medieval civil law, the Corpus juris civilis, and Gratian's decretals-cum-canon law, Corpus juris canonici, find their blossoming here. Within this century-long development and codification, the canon documents of ecclesia (decretals and bulls) and the civil laws inherited from Justinian are interpolated and cross fertilized, borrowing processes and concepts from each other.^4

During the twelfth century, in an age when disputes were still commonly settled by stone, iron, and flame, Europeans rushed to make use of new legal procedures provided by princes and popes, procedures that offered reason as an alternative to violence. Young men who had studied Roman or canon law were in demand everywhere, because they knew how to take testimony, weigh evidence, and put in writing their conclusions. ^5

Bologna university trained Lotario dei Conti of Segni to be canon lawyer after his time in Paris studying theology; and Lotario would become Innocent III. Bologna trained Lotario in the power of legal proceduralism and argumentation, of new legal ways to think which he used to great affect in re-asserting papal theocracy, of supremacy of the pope over secular rulers, and it provided many tools for formalizing, structuring, and enforcing Catholic orthodoxy 6 .The greatest expression of this juridically-inclined Catholic orthodoxy was the 4th Lateran Council of 1215, perhaps the most famous act of Innocent's papacy and giving us the legalistic, rule-bound Catholicism we know today.

It should be no surprise to us as well that out of these legally-inclined, bureaucratizing generations of the papal curia should also come that other juridical expression of Catholicism: the medieval inquisition into heretical depravity.

Not coincidental for our story of autopsy and dissection, Bologna in 13th century also became the seat of medieval medical innovation and training. For much of the early and high middle ages of Western Europe, the works of the Roman Galen of Pergamon seemed to have fulfilled such need as there was for medical theory. The exposure to works outside of Galen via the Moslems, exposure to models of scientific inquiry, provoked in Bologna a rapid expansion of medical practices.

Advent of Dissection Science

After the decretals of Innocent III, autopsy as an investigative tool takes root in medico-legal soil. And it is the city of Bologna and its surrounds from which spring the dissection as that coroner activity. At Cremona, a physician in the 1280's performed dissections on chickens and a human in order to determine the cause of a disease that swiftly passed through the region, leaving internal blisters and abscesses in common; this is reported to us in the chronicles of brother Salimbene (Chronica Fratis Salimbene parmensis ordinis minorum).

In 1289 and 1295 Bologna, examinations of corpses were ordered by the judiciary, including that of 'Bencivenne' who was exhumed and then determined by surgeons to have died of two wounds.

And then it is again at Bologna where history records the first western "medico-judicial dissection": that of a certain Azzolino Degli in February, 1302. Azzolini had just eaten a meal when he collapsed and quickly bloated up and discoloured. The family was suspicious of poisoning by Azzolino's enemies; a judge ordered two physicians and three surgeons to perform an autopsy on the body to determine the nature of his expiration. The medical opinion, after internal examination of the corpse, was that there was no foul play.^7

What exactly should have replaced it? You need microscopes for germ theory.

Medicine is a practical field of activity not a theoretical science, so people never say "we doubt the old theory but there is no new one so we will just say we don't know the explanation" the way a theoretical scientist would do. Rather, people want medical treatment, and doctors will give them treatment as there is money in it, so people stick to whatever treatment they think works until someone shows a better one and there is usually no "don't know" transititonal period. This is generally so in every field where practical applications outweigh academic theoretization.