I recently moved to a rural home in the Blue Ridge Mountains of Virginia.
I socialize with a bunch of current and former college professors, and they've all remarked on this phenomenon for nearby UVA and Virginia Tech. Interestingly, the one university in the area that is not impacted is the Christian fundamentalist Liberty University. The demographic that attends that school come from a high birth rate subculture. BYU is also not having an issue.
In fact, Liberty has had to expand. I'm not a fan of religious education, but I also think that ALL university tuitions are vastly overpriced to fund the absurdly overpaid and bloated armies of administrators. This includes my alma mater Virginia Tech.
Depends on which administrators you're talking about. The army of staff at my Tier 1.5 university make about $60-90k in an MCOL area. High-level admins make more, of course, but there's not an army of them! There's really only 1-2 "highly" paid people making >$120,000 in the whole IT department.
I'm not sure which other universities have "absurdly overpaid and bloated armies of administrators".