I think Piedmont didn't go through with the robbery because he realized that the "movement" and stealing were two completely different things. To participate in the robbery would have given those opposed to the Civil Rights Movement the justification they needed to do so. Had Piedmont participated, he would have been playing into the negative stereotype that many people have about black people. Even though Piedmont didn't like the way black people were treated, he did not seem to believe in punishing ALL white people. He demonstrated this when he felt guilty for his vengeful thoughts after the plane crash.
I think Tito told the story of the robbery as an attempt to explain where he and Skyler got the idea to rob Genie. I'm guessing he was also probably stoned or drunk- -added to the major haul they were about to take, he was very pumped up. He could also have been a bit hysterical about almost being robbed at gunpoint.