North Chicago cougar can't be that scary
If anyone knows much about the fauna of Lake County Illinois, they should realize that even in a somewhat urban area around North Chicago that there's plenty of small game to keep a large cat happy. There's plenty of greenspace around (forest preserves, ComEd runs, and railways), so there's more than enough deer, possum, racoons, muskrats, coyotes, gophers, skunks (but I don't think a cat would bother), rabbits, squirrels, and even some feral dogs & cats. So with that smorgasboard running wild that's available to a cougar, people will rate pretty low as an item of interest. Still, I wouldn't put it past a large cat to get any animal in confinement, so don't leave a small dog barking outside all night. Also if you let your housecat out and it's too dumb to hide, I can't blame a cougar for that either.
So even if the cougar rumors are true, it's not really worth worrying about. Just use some common sense about letting your pet out and not leaving it out. (And even without a cougar, its not like the coyotes aren't there. But then again, pets are fairly low on their list too.)