Don't want to throw cold water on anything,

but here are a couple things to think about regarding Michigan cougars.

Having been one of those MDNR wildlife biologists and the one in charge of all wildlife management programs and regulations when I retired a couple years ago I can thell you the MDNR policy on cougars was simple. There is no evidence of a breeding population of cougars in the state.
A couple other items to think about when looking at established populations of cougars.
1) At the time the eastern cougar became listed by the USFWS ( about 10-12 yrs ago) it was estimated there were 2000+ cougars in private ownership in Michigan.( yes, 2000 and most were in the southern 1/3 of the state) By law anyone who owned them needed to get a permit to keep them. Soome did many didn't.
2).There are a lot of sightings, and many are legitimate sightings of cougars.
3) None have been killed by cars on the highways.( possibly one)
4) None have been taken by coyote trappers
5) None have been put up a tree and photographed by the hundreds of bear hounds that cover the UP and Northern Michigan from July - Oct each year.
6) None have been shot or turned in during the November firearm deer season when 700,000+ deer hunters that are out in force.
7) At the same time other wildlife species of very limited numbers like bald eagles, moose, lynx, and wolves, are killed on the roads, killed during the hunting seasons ,and turn up in traps through out the year.
I am sure there are cougars in the state. Most likely transient animals from the west or escapees/ released animals. I for one have never doubted what peple see however, there is a big difference between transient animals or escapees and a natrally producing population. These cats move tremendous distances and it is not unreasonable that as the expanding cougar pops in the west grow, there may be more and more sightings in the UP of wild animals passing through.
Where they come from and survive in the populated part of the state is another question entirely. IMHO