I'm no expert, I suppose you're right, Byrd and his agent could conceivably come to some agreement in principle, but they'd have to get the Bills to agree (ie compensation, because they could tag him again..). The situation is the same if he has a great season; the Bills can sign him to a multi-year agreement, tag him again, trade him, or let him sign with another team with some killer compensation.
to me, it was the player may sign only a one-year Player Contract with his Prior Club that excluded him from doing anything else. You're right, the Breer article didn't address trades. I only linked it to show the changes to the tag rule (via the new CBA) that allowed teams to continually tag a player, at a cost...