I assume given it's a world history course, your professor isn't a medievalist. I'll also assume that because I'd hope that no specialist would ever say something so patently ridiculous about the medieval period. While I don't have (and don't imagine anyone has) exact percentages of the transmission of Ancient texts, I can say with a fairly high degree of certainty that the majority of Latin Texts survive via transmission through Medieval Western Europe, and the majority of Greek texts come from the Byzantine empire, with Medieval Western Europe and the Muslim world both supplying some as well.

The reason for the lack of Greek texts has nothing to do with the Medieval period's views on pagan literature. The main reason we don't have that many Greek texts transmitted through Medieval Europe is that very few people could read Greek. Throughout most of antiquity, famous Greek texts weren't translated into Latin, because of course they weren't: Anyone reading Plato was basically by definition an educated person, and educated Romans were almost universally Latin/Greek bilingual. In the west, what this meant was that when the Roman empire declined, elite language learning shifted from Latin as a native tongue and Greek as a prestige language to post-Latin Vernaculars as a native tongue and Latin as a Prestige language.

Now, many people realized this was happening at the time, and attempted to either translate Greek texts, or write new Latin texts that sort of "sum up" big tracts of Greek Philosophy. Boethius's Consolation of Philosophy is the most influential of these latter ones, at least in my period, and it has its origins in late antique stoic and Neo-Platonic thought, and was one of the main transmissions of Platonic ideas into the Medieval West. All said and done, though, this work was not enough, and many Greek texts were lost to Medieval readers in Latin Christendom. This wasn't, however, for lack of trying. Unlike Greek, though, while Latin literacy declined as elite wealth and state power did, (which, according to some research, was fairly beneficial for the average farmer) the decline was never a collapse, and it was more of a lull that anything else. By 1000 AD, Latin literacy was on the upswing again, and the textual traditions of antiquity largely continued unabated.

Now, Medieval Reception of Classical texts is complicated (Another flair asked a question about it and I typed about 1500 words of incoherent nonsense before other work forced me to give up), but the idea that Pagan texts were rounded up and burned is ridiculous. The notion that book burning was a particularly medieval phenomenon, even more so (Book burning accelerated significantly in the Early Modern period). There was a huge variety of thought on how useful Pagan texts were, but the tremendous amount of Classical references in Medieval Literature show incontrovertibly that the conclusion was, for the most part, "pretty useful."

Indeed, insofar as books were burned in the Middle Ages, it wasn't pagan texts at all, but rather modern Christian ones that were deemed heretical. Some moralists might have dislike Pagan writers, but no one ever view them as a serious threat to the fabric of Medieval Society, which they would have had to have been to justify burning something as expensive as a book. The Greco-Roman pagans were long dead, and by the 11th century when we see the huge rise in book production and writing, it was more or less accepted that all the falsehoods in Pagan texts had been safely debunked, and they could be read without much danger.

In short, your professor isn't just wrong, she's incredibly wrong. While the Islamic world is a source for Greco-Roman texts, it's far from the only one. While there might be some isolated incidents in the late antique period, and even a couple I don't know about off the top of my head, the burning of pagan books was never a systemic practice of the Roman Catholic Church. Indeed, your were correct in your assumption that they did much more to preserve Latin texts than they ever did to destroy them.