I don't know if what you said is right, but I have been basically relaying what my Latin professors have taught me and what I, as an A-student in Latin, have learnt, yet I am being downvoted. A similar thing happened to me when I started talking about Latin American literature and history.
I'm assuming most people here have gotten their information off the Web and have a very one-sided view of whatever they have decided they have attained "knowledge" on.
> The "Latin" that is generally studied at university these days comes from a mediaeval Latin that is a simplification of this old, vernacular form.
You're on solid ground to say that in the classical period there were several registers of Latin, that the lower registers gave rise to vulgar and late latin, and that those gave rise to church latin. (I can only really interpret "medieval Latin" as referring to church latin.) You're certainly on solid ground to say that speaking Italian won't let you understand Latin.
But the Latin you study in a normal Latin course is the high register of the classical period, Classical Latin. It doesn't derive from medieval Latin, it predates it by many hundreds of years.