While I have no doubt that the
Vatican holds an impressive collection of
manuscripts, I find this conclusion far-fectched. Consider this: the
Codex Sinaiticus, the most important early copy of the
Bible that we possess, is not in the hands of the
Pope, but in the
British Museum. Other important manuscripts--certainly, not all religious--are located in
monasteries around the world, and in general the various
monastic orders have been happy to let
scholars have access to them. (A great many of these were copied with
new-fangled photographic technology in the early 20th century and are thus available for public view.) Consider Bryennios's discovery of the
Didache in 1879--a massively important document not in
Vatican hands.
Without even reaching for my resources, I can say that we only have Livy's Roman histories thanks to the work of Catholic monks who were more than happy to share their manuscripts. Polybius comes to us through the Codex Vaticanus, which the Holy See has available to scholars. Arrian's history of Alexander comes to us largely through manuscripts that are now in Paris and Vienna.
As far as the idea--that this argument must contain--that there are no new finds to be found, I point to the vast collection of Gnostic papyrus material unearthed at Nag Hammadi in Egypt (the home of the largest Greek city of antiquity, Alexandria) in the 1940s, which contained, for example, a divergent translation of an important passage from Plato's "Republic". This find, though religious in nature, does help shed much light on the popular religious movements of the day, helping better illustrate the Neoplatonism that was popular among the literati of antiquity.