Even in Iberia you still have the Basques, and there's Galicia Belgica with Flemish and German. The claim your disputing seems like one of those claims that only really works at a very general level and as you point out, the non elites kind of could do their own thing and are often over looked at that level.

Your point about the eastern side of the empire is another good one. The Greek situation is complicated b/c of it's role as a language of high culture and the Semitic languages were in a state of flux anyway and going through all sorts of changes.