I can't watch the video, but I hope Pierce is angry at Doc for not putting him back in sooner. Its just too bad its in hindsight. I want him to want to be out there. He needs to be a leader of this team, and he needs to lead by example.
With that said, Doc did the exact right thing. His team had a big enough lead that he could let it ride out, to keep Pierce fresher. Pierce should have just closed the game out when he got back in there. And hopefully Pierce learned from this, and as a leader, when he sees this happening, he goes to Doc and tells him to put him back in. If he tells him the right way, Doc is not going to say no.
On a team like this, the coach is important, but they are not the leader. He is there to keep the players in check, but they are the ones who ultimately control things. Pierce needs to take that control when he thinks its important.