Perhaps we can find an answer to that question in Bernard Frischer's book "Sculpted Word"? Or maybe we can actually find Mr. Frischer online and email him a question about this. That actually strikes me as doable.
So where are we on this by timeline?
The fresco was painted in the early 1500's:
The busts from Herculaneum and Vatican were not discovered until the 1750's.
I guess we are really talking about two things:
(1) Do we have any evidence that Raphael himself asserted that the wreathed chubby figure was Epicurus?
(2) When did other people start asserting that wreathed chubby figure was Epicurus? Who was that person and when and why?
As to question (2) we now know from Joshua's post that the assertion that wreathed chubby figure is Epicurus dates at least to early 1800's. I can't read this inscription from the etching but it may or may not help with that question:
Given the dates of the bust discoveries, if Raphael knew the correct likeness of Epicurus, it would have to be based on something else, perhaps the Hadrian villa items, or perhaps well something totally unknown to us currently - and i would indeed presume that there are or were many historical artifacts in Italy and Greece that we're not aware of in this conversation.