I don't know if Americans have the worse accents when speaking Latin, but I have to say I find it particularly egregious and unpleasant ^^' It's not the American accent itself, I don't mind hearing my native French spoken by Americans for instance, but rather its application to Latin; I probably wouldn't even have wanted to learn the language had I heard it spoken only by Americans. (I should add that Latin's pronology is the primary reason I'm learning it, that's what I'm interested in the most when it comes to languages)
But I think at least part of it is cultural: for one, I'm not used to the English pronunciation of Latin, so there's that. But also, since we know roughly how Latin should sound and since I have a good knowledge of Romance languages, it may be that English pronunciation just deviates too much from what I expect, hence it sounds "bad", and certainly worse than say when it's spoken by a native speaker of any Romance language (French included, even though the traditional French pronunciation of Latin is quite off from classical pronunciation).