Facts and outside perception would say that when a school spends over $10 million to fire their coach and athletic director midseason specifically because the football team is not good enough, that school is interested in rebuilding the football program.
Facts and outside perception would say that if rebuilding the football program wasn't a priority, a school would wait until after the season for the buyout to drop rather than spending extra money and going through the public spectacle of an in-season firing so that they could get a new administration in place for early signing period.
Now, maybe you disagree with how they are trying to do it. Maybe you think they should have taken more financial risk now to or been able to secure more resources now so that we could have hired a different coach. But it doesn't make sense to say that a school which just committed a huge amount of money to buying out their coach and AD so that they could rebuild the football program isn't interested in rebuilding the football program.