I studied linguistics in university, and it was interesting learning about how languages shifted, how dialects arose and why, et cetera.
I suspect that the quote about only 1000-2000 people speaking Latin meant that only a small group of people spoke a specific dialect of Latin, with a certain set of slang and a certain regional accent. Even today in Italy, there are distinct accents and words in southern, central, and northern Italian. A bit like Californian-English versus New York-English versus Minnesota-English versus Newfoundland-English. (Linguists love to classify and sub-classify and define smaller and smaller groups - patterns make us mental with glee. This then gets misinterpreted, passed on, and the darndest statements enter the common conscious...kind of like "Eskimos have 47 different words for snow." Ask a surfer about different types of waves, and you could come away with the idea that surfers have just over dozen words for "water".)
The most interesting thing I remember from one of my earliest survey courses was a dialectical map of America. You could very easily trace the migration waves and patterns by what dialects are now spoken where.
I forget: is Latin technically a dead language at this point (only in active use by scholars and professionals, like certain clergy, rather than being taught to children as their main language), or is it still actively spoken in some tiny pockets somewhere in any form?