I'll defer to others regarding the nature of medical revolutions but can tackle the first part. The short answer is basically sort of. Kinda of. Not really. Most of that is tied up in the use of your word "all" but mostly, that theory overlooks what was happening around the rest of the world and before Christianity emerged.

For a slightly longer answer - places set aside for formal, purposeful education emerged in multiple societies. Al-Qarawiyyin and Al-Azhar were founded in 859 and 975, respectively. Jixia Academy was educating young Chinese scholars in 300. Where you're going to see different opinions and takes is around the nature of the word "university." Because Al-Qarawiyyin and Al-Azhar were founded as madrasas, some make the argument they don't technically count. Those historians or writers are likely defining a university the way we think of modern day places with university in their name: an institution of higher education that contained(s) multiple degree-granting colleges, each with a specific area of focus. That definition excludes things like Plato's Academy or the Lyceum, which fall under a looser definition of "a place where learners gather to study with experts."

Generally speaking, historians of higher education who write about the rise of formal, specialized, or tertiary education (it follows primary [grammar] and secondary [high] school) write about the feedback loop between education and a society's needs. That is, it's more accurate to say the general consensus is that as civilizations expanded, the transmission of knowledge through proximity was no longer sufficient. Instead, they needed places for people new to a topic or idea to learn from people considered experts in that particular topic. Although it's not a straight line, this notion, in effect, gave rise to formal education, then specialized formal education, then to formal education in stages of education corresponding to learners' ages, then to institutions serving a particular goal or meeting a particular need within a society. To be sure, the rise of higher education was influenced by Christianity and the Catholic Church and buildings that were created for or modified to become part of colleges were influenced by cathedrals.

Which is to say, if someone defines "transportation" as "a mass produced motorized vehicle with four tires" they could claim Henry Ford invented transportation. The inventors of the horse-drawn buggy, boat, and bicycle, though, would likely beg to differ.