As rare as the North American Elephant.. interesting. Apparently there were five different species of north American elephant around 13,000 years ago. Not terribly rare at all as it turns out.
Now I'd imagine in the era of the mega fauna, there was likely some bigfoot or bigfoot-like creature wandering about. The lack of fossil record is not major concern considering that fossil records are not complete. And I do believe we have enough fossil records of similar species that at least warrant a 'plausible' for the Sasquatch beast.
Native Americans have had their tales of bigfoot which predate the arrival of Europeans. So if you figure that extinction dates are far from accurate, doesn't it seem plausible that some 5,000 to 2,000 years ago could have been living in the same land as a dwindling population of bigfoot?
I don't know. There are plenty of larksters and charlatans that destroy any credibly of sighting claims. But some time you find an individual who has experienced something inexplicable and they are left with no other choice than discussing the 500 lb gorilla in the forest.
Like I said before, I can't imagine any sane person who wishes to make the statement that they saw bigfoot. However, sometimes it's what you got.