My wife is from Le Flore County, OK, last time I was there with her visiting her family, one of her cousins told me about seeing a mountain lion.
I would agree with you, in that I don't like coyotes, but would much rather have them around than big cats.
The wildlife officials, are the same in most other places too. Here, they say they aren't here, and even though two have been killed in the state in recent years, one hit on a road, and one actually shot by a wildlife officer. The official word is that they were likely brought in or escaped. Couldn't possibly be that they traveled on their own, in a natural range expansion, like bears have done into this area. I know several people that say they have seen mountain lions.
Years ago, there were no bears here, but were in the mountains to the east and southeast KY. There started being sightings of bears here in the County and a couple got hit on different interstates.
The official word was that it was just young males roaming, and that there were no female or resident bears here in this part of the state. A neighbor caught sight of a female and cubs on his trail camera, at the same time they were saying that. Now its not unusual to see bears or signs of where they have been.