As a special assistant when there was a possibility that Bill himself might be suspended for a year. He had no one reporting to him. Pees's leaving a year later was not to make him DC. If that were the case doesn't hr "choose to leave" when Capers is here, not after he left?
I hadn't heard that particular rumor before, although I researched it after reading your comment and apparently there was scuttlebutt about it including on this forum. Personally I have a hard time believing that Kraft and BB would have had a complete outsider run his team during a suspension -- that's far, far, far "worse" than having a complete outsider brought in as a coordinator. The culture is completely different. The players wouldn't respect this guy as he's the equivalent of the substitute teacher. This isn't Bruce Arians, an internal guy, taking over during Chuck Pagano's cancer battle in 2012. This just has disaster written all over it.
Capers left after 2008 to become Packers DC. Point is, I think Capers was brought in as someone who could mentor Pees because Belichick hadn't been impressed with his work yet. Capers still had a different system, and so left after 2008 to pursue it. And BB wasn't happy with Pees by himself again in 2009 so they agreed to part ways.
Belichick and Capers didn't have much of an outside relationship prior to this. Contrast this with Kelly, who's been one of Belichick's go-to guys for the last decade even though he's never worked with him. The no-huddle offense the Pats instituted in 2012 was based in part on Kelly's success in college after they had a meeting that offseason, although it was definitely changed a bit to be more similar to Buffalo in the early 90s.
If Belichick doesn't think anyone on his staff is ready to take over as OC, Kelly is a guy he trusts, and if he thinks Kelly can continue to run *BB's system* with his own tweaks, I think he'd take him. If Kelly wants to run his own system with BB's tweaks, I don't think the Pats would hire him.