LAC's by Rhodes scholarship winners

I’m afraid you have it wrong. The Rhodes website itself confirms that students are eligible to apply in the state where they attend college (not just their home state). The Rhodes website also confirms that (1) schools in states with little competition have an advantage, and (2) schools with national recruitment have an advantage.

As noted previously, Reed – which is a top performer on your list – stands out in both respects.
http://www.rhodesscholar.org/winners/college-and-university-winners/