my grandfather was raised near Black mountain Kentucky. I remember him telling me that two mountain lions were killed by hunters there back in the 30's and pictures were actually printed in the local newspapers. He recalls hearing them at night and he described the noise as a woman screaming. He was not the kind of man to make up a story like that.
I also recall another story, in the National Geographic I think, about the tremendous hunting ranges that mountain lions out west are said to had. Tagging on in one state and having the animal turn up captured or dead one or two states over is not uncommon. Anyways, they had a map of known ranges, approximate historical ranges, and areas where mountain lion bones, carcasses, or stool had been found and documented. That area my grandfather was raised in in Kentucky fell under that last range where documented evidence had been found.
My opinion is that they are out there.