Look at Coach Pete. He had a very comfortable life at Boise State. But the chance to compete with a better pool of talent in a different environment got him to go.
I personally know a number of professors at BYU that have turned down offers from ivy league institutions to teach at BYU. Don't doubt for a minute that an LDS coach wouldn't jump at that, even for less salary. Maybe not all of them. But people do it all the time