I think Cozens was DFA'ed and then released. He likely cleared waivers. Also, we (myself included) are forgetting he's basically out for the season (despite his protests) so I doubt any team wanted to acquire him. So it almost doesn't matter if he asked for his release (or was entitled to it), it was probably just a courtesy, let him get on with his plans for next year (and maybe he was going to be a minor league FA this off-season anyway?).
Actually seems a little unfair, does he lose the remainder of his AAA salary while still being injured? Does going off the 40 decrease his salary in the minors? And can you even release an injured player who got hurt working for your organization? If not it probably was at his request, maybe there was even small payout.
I still think they will get something for Williams, even if it's just a different kind of bench piece or depth relief arm. Or perhaps he'll be folded into a bigger off-season deal.