Yes, Pitino deserves some credit as well.
The way the buyout works he would have had to stay unemployed for a while (probably a couple years at least, but it depends on the finer language in the contract) in order to collect the full $1.75M. It’s not just “here’s a check for $1.75M. See ya later.” He would collect that in installments over a period of time, and the payments would cease as soon as he found comparable employment.
Coyle could have fired him walking to the locker room after his last game on March 11, and if he was hired at New Mexico on March 16 (as he was) we wouldn’t have had to pay a buyout of any kind. But because Coyle let him know earlier that he probably wasn’t going to continue as our head coach he was able to get a head start on looking for other jobs. Plus, it shows him respect, and may put him in the mindset that we are trying to help him find another job so there is no need to sit at home and collect our money.