We will never know how Philidor would have played had White played 2.Nf3 because there are no recorded games where Philidor had that position. Did he spot a flaw in the idea? The Count was impressed with Philidor's game, so later that year he played the Philidor defense against Atwood.
Philidor plays the Philidor

Philidor seems to have spotted a flaw in his defense. He played the same Atwood several times and mostly used the Sicilian (played of course, Philidor style nothing like the moderen Sicilian) Here is a blindfold game against Atwood by Philidor:
Philidor had a very different concept of how to play the Philidor Defense than we have today. He intended to play a quick ...f5 and dominate the game with a broad mobile pawn front.
One of the earliest examples of the Philidor is his game against Count Bruhl in 1792.