While the Democratic Party had undergone a LOT of changes between FDR and Reagan's rise to prominence, I do think that some of that quote was a bit of political acting on Reagan's part - he was a lot more liberal in rhetoric during his younger days, trashing basic tenants of conservative ideology that he would later champion.
Any time anyone says "I didn't leave X party, X party left me" that person is automatically suspect in my opinion.
It's suspect if they immediately run to an opposing party and become a propagandist for them, as Reagan did.
