I think you might be going out on a limb here to compare TM to TF with respect to the media. Tommy was a Communications major so he was at least prepared somewhat to deal with the media. Also Tommy never did have to defend a loss like Wisconsin or Michigan. Another point is that I perceive them to be very very different personalities. From what I have read about TM, he is a very private person and some of the players close to him have said that he is almost bashful or shy and that is often confused with aloofness or even arrogance. IIRC, when he started as a freshman, he was so soft spoken the coaches had to teach him to call out the plays with more volume in the huddle to make sure everybody heard the play.
Tommie had the confidence to go in and take charge. Taylor hasn't shown that yet. I hope he does at some point.
The other point about Frazier and Martinez is that they are worlds apart in the respect fans have for them. I am going to guess that there is probably nothing that TM could say that would change some peoples mind about what type of quarterback he is. My gut feeling is that he feels as though the only way to change anyone's mind on that topic is to do it on the field. That is why he is dedicating so much time, effort and money to improve.
I think that people would actually like to hear it from him for a change. I'm not just concerned about his footwork or his throwing motion... what kind of a person is he? Is he wanting to take a leadership role? Has he done so? We hear from his teammates, but never from him.
There are some that enjoy the spotlight and others that cringe at the prospect. You mentioned fear and that is dead on if by that you meant fear of speaking publicly. That is my perception of Taylor Martinez with respect to the media. He has enough on his plate without the burden of trying to convince the media and critics that he is a really good guy. And like Hutto already mentioned, can you imagine the presser if he was one of the three. It would be turned into a sideshow with the guys wanting to get a headline from him on his "improvement" over the summer. I think Bo anticipated a fiasco and wisely avoided that confrontation by taking the guys that like the limelight.
I think that this type of sideshow could have been avoided if Taylor had made himself more available over the last two seasons. If he has a problem with public speaking, now is the time to work on it. His "job" is secure right now... it may not be when he enters the real world. I don't know what he plans on doing with his life, but he's majoring in Advertising. I am guessing there will be some interaction with the public (as well as clients/bosses) in that line of work.