I've heard that collared cougar story a dozen different times from a dozen different people in the last year. It's always a different county, different person who shot it (usually a friend of a friend, or my cousin's brother in law, etc.), with slight variations on the theme - sometimes the cat is buried out back and the DNR comes knocking on the door looking for their radio collar, sometimes its in the barn when the DNR comes for the collar - you get the picture. Can we say urban legend? I'd be willing to bet this story crops up in surrounding states as well.
As far as where the cats are coming from - the Black Hills is the closest wild population. They do roam pretty far and the rivers make great travel corridors. There's probably a couple of these wild cats in Iowa right now. Most though are pets that either escaped or were dumped on purpose. You'd be suprised at how many people buy mountain lion kittens for pets (illegally) and then figure out how much work they are to feed and care for...