I think it should occur to everyone that before he knew the tag would be used on him, he would take pain medication and tough it out in a contract year where he knew he was going to have a once in a lifetime earning opportunity. It also should be clear to anybody that in this situation where the team isn't prepared to commit the value he believes he's worth, he might feel like he shouldn't play until he's healthy so he doesn't aggravate that injury and further jeopardize his earning power. He's within his rights to do so and if the team were telling an injured player to play no matter what, the NFLPA would and should be all over it.
I don't know how these things heal or why it has taken this long to do so, but I also doubt Byrd has been sitting around eating chee-tos and watching TV a la Jason Peters.
I agree that if he is faking the injury it's a bad faith move, and it would be a black mark on him and Parker. That's exactly why I don't believe he is faking it. Such a move would be more likely than not to backfire.