I don't think it's crazy to assume that part of this signing is the Putin strategy of sewing (additional) dysfunction in a rival's front office. BB knows that the Pegulas are relative simpletons who will turn the screws on their inexperienced GM for shelling out $3.5M for a two-week tryout, only to cut bait and let the division rivals pick him up. BB loves beating the Bills over the head with their own, old shoe. I'm convinced that the Gilleslee signing was palatable to BB because he knew that, even if TD Mike didn't work out for the Pats' offense, he was thwarting the Bills' plans.
The Coleman experiment is an embarrassment for Beane who is in over his head and has not shown that he has any real strategy or understanding of how to build a roster or manage his bosses' money. Those bosses surely have noticed by now.