Sorry, I haven't read the article or the comments in this thread, but it must be somewhat tough in that position.
After all, guys like John Elway and Dan Marino would be asked constantly about what it meant to not win the big win. The two would say that they are striving for it, but that they didn't need it to validate themselves as great players and would be okay without it. That it's a team game and that not everything is within their control.
Well, obviously John Elway DID end up winning a Super Bowl (eh, 2) and was asked about these previous responses. He ended up saying something along the lines of "Who are we kidding, THIS is what it's all about. You can't consider yourself a great player without a ring."
It's much easier to change your tune when you do have a ring. In LT's case, he doesn't, so it's not entirely surprising that he would try to downplay the importance of winning a championship.