I think it's important to remember that there are two things being spoken of here. The first is the relatively unlikely, easily mistaken, but remotely possible event of seeing a cougar. The second is the event of seeing an Eastern Cougar, which is not possible because they are extinct. Remember that there was a recent event in which a cougar was run over by a car in Connecticut. The cougar certainly did exist. It most likely had been seen by numerous people, and there's even a possibility that others are out there. Many people over the the years have reported seeing cougars in the woods of Connecticut. After all, I've only ever seen one dead bobcat on the road here in Vermont in decades, but there are plenty of them out there. They're elusive and street smart, but they exist. I've only ever seen one lynx at all, but even though rare, there is a real population of them. So yes, perhaps, maybe, on a long shot, one might have seen a cougar. That claim can be doubted and contested and the likelihood is high that it is a mistaken identification, but it's not outright impossible. But the claim of an Eastern Cougar is in a different dimension.
For as long as I can remember, even back to the 1950's, people have reported seeing cougars in New England. My Vermont relatives up in East Montpelier reported a "panther" when I was a kid, and who knows what they saw? People still report the occasional sighting. But those are just stories without a body. The only body I know of confirmed that a cougar existed and that it wasn't an Eastern Cougar.