I halfway wonder if Belichick offered a bit of a mea culpa during the postgame meeting with Brady. Perhaps seeing what Brady is doing in Tampa leads him to believe that Brady earned the right to have the team commit to him through 'x' age. That's one line of thinking.
The other approach is that Belichick didn't apologize, necessarily, but basically said, "look Tom, I love you, like, seriously - you mean the world to me. I know things didn't end perfectly and I'd like to sit down at some point in the future and talk, hash things out, reconcile, and I acknowledge I could've done some things differently. It genuinely bothers me that our relationship is being talked about as anything other than strong. If I ever wasn't great about demonstrating my appreciation for you as a player and for the things you did for this team, I feel bad about that. I love you so much, bud, and I want you to know that.".
Who knows, but that's kind of the vibe I'm getting. Other than losing (and the dents in my drywall), that was a really fantastic game of football and it highlighted the best in Brady and Belichick, respectively.