I believe that you start the best guy at every position. Then it's your job as a coach, and it's the responsibility of the players - especially the "leaders" - to build team chemistry no matter who's on the field. "The other players like him more" isn't a valid reason to start a guy.
I agree with the bolded part.
But I disagree with the rest. Chemistry is all about who's on the field and how the players interact with each other. A team can have great chemistry even if they don't like each other. And how do you quantify who the "best" player at each position is? I'd say it's whoever gets the team more wins, regardless of how explosive or athletic a guy is. And chemistry definitely has to do with winning games.
There are plenty of ways to quantify who the "best" player at every position is. Coaches are constantly assessing their players during drills, scrimmages, meetings, in the film room, and eventually on gamedays.
The real question is, how do you quantify "chemistry?" Especially with known and unknown quantities like Lee and Martinez were. If Martinez getting the start is what disrupted team chemistry, then how do you know it'll disrupt team chemistry before the decision to start him? And once you decide to start him, do you go back to Lee when you see that some of the guys don't like him as much? What about the chemistry problems that creates - you're then benching a guy not because of his play on the field, but because of whether other guys on the team like him or not. How do you run a Division 1A program like that?
Why don't we look at it this way - everybody has said that Martinez has really grown into his role this summer, and become a leader on the football team. He, at this point, appears to be a central key to the team's success this season. But say that we get to the end of fall camp and Brion Carnes emerges as the better QB. To bench Martinez at that point would disrupt team chemistry, but Carnes has shown that he's the better player on the field. What do you do?