deserved a spot in the big12 were a few Texas politicians. Houston historically has not been a strong programs. They don't, or at least haven't, drawn many fans, they don't make much money, they rely heavily on taxpayer subsidies, etc. And now they don't have the coach that gave them those couple of good seasons.
So, no, I don't think Houston was close at all to getting in. None of the other applicants come anywhere close to BYU in terms of program strength (revenue, fan base, facilities, etc.).