KYOU's transmitter is actually in the Cedar Rapids-Waterloo DMA. I wonder if they attempted to become a two-market FOX affiliate in the early to mid 1990s when KOCR was in awful shape (that station was in such dire straits that they sold the NFL rights to KGAN for the 1994 season).
Here's likely why KOIA decided to affiliate with FOX instead of CBS or NBC:
At the time KOIA first came on, it appeared that the Quincy-Hannibal and Kirksville-Ottumwa markets would merge to form one large market (they were complimentary markets, as Kirksville-Ottumwa only had ABC (KTVO; which briefly moved their tower closer to Hannibal and Quincy before retreating to its original tower after the new one collapsed) while Quincy-Hannibal had CBS (KHQA) and NBC (WGEM); ABC in the Quincy-Hannibal market came from KTVI, KTVO, or WQAD depending on location while in Kirksville-Ottumwa, CBS came from KHQA, KGAN, KCTV, or KCCI and NBC came from WGEM, WHO, or WDAF