I think the media will try, but they will get bored quickly when BB doesn't fuel the fire. The problem last year was Rex Ryan talking all that stuff about "secret Tebow packages" and about how they were going to use him so creatively. Also, in Denver and NY, the starter was questionable. In NE, Brady is unquestioned. I think the only chance for this to get ugly is if Brady gets injured and the discussion turns to Tebow vs Mallet. Even still, I think BB will handle it well, even if Mallet gets the start... but Mallet will be under immense pressure to win, not just from the media, but under personal pressure to prove he deserves the starts.
As a Tebow fan also, I wouldn't question BB if he started Mallet over Tebow. I have so much more respect for his decision making than Fox or Ryan. I feel as though if he says, "Mallet gives us the best chance to win" that it is genuine. Tebow is the 3rd string QB, and I have no expectation that he is going to play QB this year. I do think BB will have a competition for #2 and #3 this preseason though. It's plausible, but unlikely that Tebow will usurp Mallet's position.
Unless BB has a tattoo of his wife wearing a Ryan Mallet jersey on his arm, this should be a non-issue.