What you say makes a lot of sense to me. You are right: if the Romans loaned the word for "violet" this must have been at a rather early stage. To crosscheck your theory one would have to look at other Indo-European languages (which ones? I don't really know much about those things) that have no or little connection with Latin or Greek. If the word for the flower resembles (f)ion, your guess is right.
On the other hand I have read a bit about the meaning of the violet with the Greeks and the Romans. And this sounded like both the mythological and the practical use (for instance as medicine) were taken over from the Greeks by the Romans (Der kleine Pauly, "Veilchen"). The Greeks seem to have cultivated the violet for those purposes and the Romans copied that (that's at least what my dictionary says).
Is that theory (Latin > Greek) really overdone? I'd like to learn more about that. Got a link?
Thanks for your efforts!