I think he showed the ROI model of championships to the state of Alabama, the University Board, and the Tuscaloosa City Council. Winning is secondary to winning it all, by far.
There you go with that silly theory again.
Alabama is not a good example for you. Bama was Bama long before Saban got there, and they would still be Bama today even if they had never hired Saban....although with fewer championships.
I cannot imagine the REC ever telling Saban - or any Head Football Coach - "No, we can't do that for you." They have wealthy boosters falling all over each other trying to feel important by donating whatever is necessary. Along with a lot of money that isn't necessary.
I'm not sure why you're "convinced" Saban used his own money to pay players. It's certainly possible, I just can't see him needing to that. Maybe if a player came to him needing money ASAP, but even then I think he could have easily asked a booster to reimburse him.