Welker has confirmed that his words were in jest. This is nothing new for him. He has a Kevin Millaresque streak of silly commentary.
What convinced me that Welker was just joking is that he said anything at all. If there truly were a serious rift between Welker and Belichick, I doubt Welker would be absolutely silent on the matter, then air his grievances during a post-game interview, then call his remarks a joke. It doesn't make any sense.
I'm sure Welker wasn't happy about Julian Edelman essentially being promoted above him on the depth chart. I think everyone in New England apart from Edelman, Josh McDaniels, and Bill Belichick was unhappy about that. It was a mistake. I don't think there was an ulterior motive behind it, such as punishing Welker for holding out or trying to reduce his free-agent value for 2013. I think the Patriots saw something in Edelman that never materialized during the games. The decision was wrong. Simple as that.
But Welker has materialized now that Edelman has been sidelined by injury. In the first two games of the season Welker caught 8 passes for 109 yards. Since then, he's averaged 10 receptions and 125 yards per game. And he caught his first TD of the season on Sunday.
So it seems as though Welker has definitely earned his job back. That's good for the Patriots, bad for the rest of the NFL.