TL;DR - Dray has every right to talk trash to Pierce or anybody else he feels like doing on the court.
Outside of Paul's scoring, from a sheer accolade standpoint, Draymond has done much of everything Pierce has (NBA Champion, 2nd Team All-NBA) in less than half the time it took Pierce to do it. Pierce got some 3rd Team All-NBA selections on his resume, but he's never been NBA All-Defense, like Dray has done twice over. He's never won a gold medal like Dray has. He's never won DPOY, which Dray will likely do one day (and should have done once already, no disrespect to Kawhi).
People in here act like Draymond is some bum ass nikka when in all actuality, he is probably the most versatile player, the defensive anchor/engine of and -- by most popular accounts -- the heart and soul of a team (the same shyt they'd say about Pierce during his twilight days in Boston) that has been historically good in the past three seasons or so. Like he didn't average 17/10/6 to go with two blocks and a steal per game in last year's finals. Like he didn't put up 35 and 12 in a game 7.
I suppose some of the same people in here going at Draymond's throat think that Chris Childs should have stayed in his lane instead of bowing up at Kobe in 2000 because "basketball reasons" or something