Florio at PFT explains it pretty clearly. If Branch is going to win a grievance it will have to be for breach of contract.
But there are two difficulties. First of all, it is very unlikely that the terms of any verbal agreement (if there was one) would be sufficiently clear for there to be a contract. Secondly, one of the principles of contract law is that there is only a contract where there is "consideration" (something given in return). But even if the Pats promised to let Branch take a decent offer if one came along, there would be no consideration because Branch did not offer anything in return.
Florio is a lawyer and knows about this stuff. I'm not but it smells of b*llsh*t to me.
Florio's view is that the idea of letting Branch seek a trade has blown up in the Pats' faces because, whatever the legality, the fact that there are offers in excess of what the Pats have offered will reinforce Branch's sense of grievance. That's an interesting and plausible interpretation, it seems to me.