Here's a totally silly possibility, but given how long this is taking why not throw it out there. It's not unheard of for a team to make a trade, even within the division, for a player with the transition tag. That is how Wes Welker was traded to the Patriots. Of course back then the Poison Pill was still legal, and the Patriots had added Poison Pill wording to the offer to Welker who the Dolphins had applied the transition tag to. (If Welker played 4 games in Miami in the first year of the contract, the whole contract would become guaranteed. So, if Miami matched the contract, Welker being a Dolphin, would, barring injury play 4 games in Miami, thereby automatically guaranteeing the entire contract, something the Dolphins did not want to do). In the end, the Patriots decided instead of adding the poison pill wording, which had caused friction between organizations in the past, they would work out a trade with the Dolphins.
Now, obviously the situation here is a different, and poison pill wording is no longer allowed, but what if Clay just doesn't want to play in Miami? It doesn't matter why, maybe palm trees make him queasy, or perhaps he's allergic to bikinis, or maybe he simply thinks Buffalo is a better opportunity to win a Super Bowl. Whatever the (hypothetical) reason may be, let's just say for the sake of argument that he wants out of Miami. Well then there would be an issue because if Miami matches Buffalo's offer, Clay is stuck in Miami for however long Buffalo's contract offer was for, he would basically be being forced to stay with an organization he wanted no part of. In that situation it would make sense for the all three parties to work out a deal. Clay gets out of Miami, Buffalo gets the player they want, and Miami gets compensation. Crazy, far fetched, and completely hypothetical? Sure. But not impossible.