re: But there's a long shot...
True.
There have already been several IR searches for such a 'Nemisis' object. If it existed, it should have been found. The odds are very long against another even fainter Proxima more proximate than Proxima.
Possible low proper motions and the lack of paralax measurements of all the myriad faint red objects is just why RECONS is really 'discovering' known stars that happen to be close by, i.e. within 30pc.