Well if memory serves, La Tech was an independent through about 2001. During that time, the monstrosity that was the 16 team WAC broke up and the half that included BYU, Utah, Wyoming, CSU, UNLV, New Mexico, UNLV, and San Diego State left to create the Mountain West Conference. Back in 2001, the Sun Belt Conference was formed for football, but the WAC had an opening or several. So in ‘01, the WAC added Boise State and La Tech.
While the Sun Belt makes a lot more sense geographically for them—hell, even Conference USA would work a little better—they might have been thinking that they would have a little better exposure playing in the WAC than the Sun Belt.
Anyway, that’s my best educated guess going completely from memory.
Don’t ferget Air Force.