The Thing loves to stir conflicts and point the finger. Watch Palmer and Norris when Macready is trying to get inside when locked out. At that point they’re fully assimilated and are diverting everyone’s attention.

So, I see it as a very logical theory that the noose was used by Blair since he knew the implications and when assimilated, it tried to use the imagery of the noose as motivation for Mac to let him back in otherwise he’ll “commit suicide” which has already taken place.

After all he feels “much better now.”