Ok, I'll try to tackle this one. Obviously, we can't be sure about the trustworthiness of the Archive of the Holy Office (which is separate from the Vatican Apostolic Archive, even though the same thing can be said of the latter), but this is true of any archive - e.g., those containing the records of the Stalinist period in Russia. Anyway, I'm going to provide some examples and make some arguments to give you an idea of how historians approach these archives and why they, with some caution, more or less trust them.

The Holy Office (or Roman Inquisition) was established in the sixteenth century as a bulwark for the Catholic orthodoxy aginst the Protestant Reformation that was sweeping the continent in that period. The former "Medieval Inquisition", established between the very end of the twelfth century and the beginning of the thirteenth century, had been a much lesser monolithic organization, that by the way was not active in large parts of Europe (for example, Castillia, Scandinavia, etc.). I'm focusing on the Early Modern Period but, again, everything I'm going to say can be applied to the Late Middle Ages (for what it's worth, Early Modern Europe was in many aspects way more violent than the previous centuries). In theory, the Holy Office had jurisdiction on all the Catholic world, but de facto was limited to Italy - the parts of Italy that were not occupied by foreign powers, especially Spain in the period (1500-1700). So, Sicily, Sardinia and other territories were under the jurisdiction of the Spanish Inquisition, with regards to religious and even what we see as non-religious crimes. Moreover, the various local Inquisitions (e.g., those of Modena, Pavia, the Venetian Inquisition, etc) had to give copies of their records to the central Roman Inquisition, but this didn't happen always. We have to rely on local archives more often than not, and these archives are by no means complete.

That many archives are not complete is a commonplace situation with which historians have to deal with. I've read too often on the Internet (historical illiterate) people comparing, for example, a huge death toll for the witchcraft or heresy trials calculated a century ago and a much smaller figure for the same things calculated in the last forty years and saying that historians are morons/bribed by the Vatican/apologists/or so naive to be oblivious to the "obvious" facts that in the last century the ecclesiastical authorities have destroyed a lot of records. Of course, historians are not idiots (not all, at least) and know very well about the loss of information happened not in the last, but in the last three or four centuries.

For example, we know that a lot of records were deliberately destroyed at the beginning of the eighteenth century by the parlements (local civil courts) of Toulouse and Bourdeax in France; and this is particularly annoying to historians of witch trials, since the vast majority of these trials in France happened under the jusdiction of these tribunals, fewer in other parts of the country. So, when lacking such records, they have to use other data to make some approximate estimate of the number of trials and condemenations (even if they are more interested in knowing how the tribunal worked etc, not just these raw data). The archives weren't suppressed because of religious reasons or because they had entered the century of the Enlightenment and suddenly felt ashamed of what they had done: the reason was a complex strife between these local courts and the central parlement of Paris, to which they were supposed to communicate their work and send copies of the records of the various trials (and for the French parlements, these included also mundane secular crime, not only witchcraft and similar things). The trend to centralization in the Modern Period and the fact that the central authority - eager to rein in the political power of the provinces - usually preferred to limit to the minimum the number of witch trials in particular, made the local and peripheral authorities (more prone to execute people with only the slightest evidence) exceedingly discontent; and the latter didn't have problem to suppress records of trials made in an illegal way to avoid investigation of fuctionaries sent by (in the case of France) Paris.

For the same reason, the Spanish Inquisition, under the political control of the Crown, has incredibly complete accounts and records in comparison to other Inquisitions, with however some inevitable big gaps (also because it prosecuted a long lists of crimes, from conterfeit to pederasty); however the archives of the more peripheral tribunals (especially those of the New World), are in lacunuous condition. The most complete archives existant are those of the Portuguese Inquisition, Goa excluded. As for the Roman Inquisition, the problem is that they were devastated and dispersed during the Napoleonic occupation by the French troops. With these examples, I'm not saying that there haven't been destruction of records for religious reasons (there are some references to the bishop of Benevento burning documents out of fear for the anticlerical sentiment during the Risorgimento), but archives can be dispersed for any reason (in the bombardments of WWII, for example). Anyway, if the records of a process that ends up in a condemnation to the stake get lost, it's still likely that at least this condemnation remains in historical sources. In Italy, as I said, Inquisitors, local civil authorities and even other ecclesiastical authorities outside the Inquisition like the bishop of a city, were often at odds with each other, so if the Inquisitor suppressed the record of a trial for some reason or another, we can often know about it from another source. An auto da fé that ends in a bonfire hardly passes unnoticed, since they were held in cities and in plain public sight, not hidden in the woods. Especially in big cities, the civil authorities, an ambassandor or a foreign visitor won't certainly omit to write about it, even in passing. The problem is with trials which didn't end up with death but minor penances or acquittal (i.e., the overwhelming majority).

So, the death toll of, for example, the witch hunt, a century ago was in the hundreds of thousands or millions simply not because there were more records than now, but because the scholars didn't even look at the actual documents, it was only guesswork. The "9 million burned witches" figure that often I still see somewhere was "calculated" by an eighteenth century historian in a way that I won't report here unless asked to because it's so absurd it would taint the rationalistic image we all have of the Enlightenment.

Now, about the trustworthiness of the extant records. Leaving aside the millions of boring bureaucratic documents, I'll just say that there is still a quantity of politically or religiously embarrassing and unflattering information that if the Church has tried to "sanitize" them she has utterly failed. Not long ago David Kertzer published the book The Pope and Mussolini, after long researches in the Vatican Apostolic Archives, and no, the book is not pro-Church (whether it's an accurate book or not doesn't interest us). Apparently the sources to which Kertzer had been given access hadn't been properly "corrupted" or in any case there were still unflattering data he could use to write that book. Regarding the Inquisition archive, anyone who has had the pleasure to read an original transcript of a trial (even those with torture included), knows how incredibly detailed are they. In the late sixteenth century those wrote those records didn't think: "Oh, here let's write we've used a very gentle waterboarding instead of the strapado so those stupid historians of the future will think better of us". And they were not (and could not) feel ashamed of what in their days the vast majority of people didn't consider particularly shameful. They didn't feel judged by people living 300 years in the future. They wrote detailed transcript and followed strict rules because most of them actually and sincerely cared about a just trial (and no, this is not an apology). Of course, abuses of power and illegal trials (like that of Fulgenzio Manfredi) still happened. But at the end of the day we can say that the extant documents more or less reflect the historical events faithfully. Sometimes historians must use a more skeptical approach, but this is valid with any kind of historical document.

Further reading:

Christopher Black, The Italian Inquisition. The better and most up-to-date book on the subject available in English.