Is the Eastern Cougar extinct?

The US Fish and Wildlife Service has decided the answer is "yes." While agreeing there are some confirmed sightings, they have put all these down to escaped/released pets or, in states like Illinois, cougars sneaking back in from the west.
The obvious question is, "If there's a confirmed sighting and the cat is not caught, how do you know where it came from?"
The FWS experts rely on the theory that a breeding population should have left more evidence than we have, but I don't know. This is a pretty darned elusive animal. I suspect the extinction label is premature.