"National search" means that the job is open and the direction the program will take is up for debate. Of course, the successful applicant might have some connection to MU, or to the region or state, past or present, but that does not mean a national search did not take place.
We learned (were told) that on the men's side, the new coach had at some unspecified time in the past been designated "coach in waiting", and no real job search was done at all.