Although I can see how you might be right, I still think that "parlare" means the act of moving your mouth to speak words while "dire" means the actual sounds that are coming out of your mouth.
Shoot for all I know "parlare" could simply be a more polite way to say "dire"....
I would say it's technically incorrect. Think of the English equivalents: "They say a lot" vs. "They speak a lot". They seem like they mean the same thing (you can't speak without saying things, but you can't say anything without speaking), but the connotation is slightly different.
"John says 'hi'" vs. "John speaks 'hi'".