Bull Gators have no pull anymore, that ended long ago with big money from TV contracts. If Bull Gators had any pull over the last 3 decades we wouldn't have gone through the last decade that we have.
I think you’re both right and wrong.
Here’s why, Stumpy Harris (major Bull Gator) was quoted by Bianchi supporting keeping Muschamp in 2014.
In 2018, I heard Tony Barnhart address the Orlando Touchdown Club and he told me that he knew Mac would be fired well before he was because a major booster had pulled him aside early in the season and said something to the effect of “we need to get rid of this guy”. It was a matter of time and building against the National optics of firing a coach after winning the East two straight seasons. Mac weeks later said “death threats” and that was it.
Now money does play into it, but those two examples show that there is some workings behind the scenes where boosters still matter. They might not have the pull they once did, but they still have influence.