0.01% chance that Diaz trusts Perry. If Miami had brought in a new HC, then Perry might win the position. Diaz witnessed Perry's terrible decision making, on and off the field for two years. You are underestimating how much that will factor into Diazs thinking (and if you think that Enos makes the pick without Diaz having to sign off, you are wrong). I think the coaches want Martell to win the job, but they aren't going to hand it to him. If Perry beats him out by a sizable margin, then Perry deserves to start. If they are close, tie goes to Martell since Diaz knows what he is getting out of Perry.
It was previously reported that Perry and Jarren didn't even start studying film until Martell arrived and they saw that he was constantly in the film room. During games, the Center had to make calls that Perry was supposed to make but couldn't because he hadn't done his homework. Preparation leads to success. Perry is more talented but Martell knows how to prepare. Coaches want a qb who is basically a coach on the field, and it is highly unlikely Perry suddenly developed the study habits of Peyton Manning.