Ooops right that article is from Jan 2010, so I got the season wrong thanks.
That's the season we got demolished by the Ravens in the wildcard round, in Foxboro.
Still, it speaks to the OPs point. Welker, in the 2009 season, was a cornerstone of the offense.
I'm just saying that it isn't like people don't get hurt in the last game of the season. That is, it isn't crazy to rest people: it's football and people do get injured.
Whether that potential cost outweighs all the benefits of playing people is another issue. I tend to trust Belichick, and think it depends on the situation/player and their current injury status. The Welker thing was a complete fluke: whether that makes me more likely to say "Rest them" or less likely? Not sure. Do we want Edelman going down on a complete fluke? Obviously not. But that's the risk we are taking, for what benefit?
If we were playing for a bye, or for a playoff spot, then clearly we fight like hell. In this case, it's a little more fuzzy. I tend to be on the side of PLAY and FIGHT. Look at last year's debacle in Miami.
But I just wanted to point out the Welker situation as food for thought.