Pretty spot-on.
For much of its history, the University of Florida was the school for white males. White females had to go to F$U. Blacks had to go to FAMU. As such, neither school could compete in Division I-A football, the only competition that The Gator had in-state was the University of Miami. And when Miami, in a budgetary crisis, tried to open a conversation about becoming a state school (as some private schools in other states had done), we got vetoed by the University of Florida, (in part) since AT THE TIME Miami was probably a more recognizable geographic name than Florida was. And Florida does NOT like to be eclipsed by any other institution.
So, yes, Florida clings to being "the flagship". To being "the first". To being pre-eminent. To being the only AAU school in Florida for nearly 4 decades. To being in a conference that has become powerful due to southeastern migration and the rapid growth of populations in nearly every SEC footprint state.
I can respect academic excellence. Harvard is great. Yale is great. Stanford is great. But they didn't become great by sucking a disproportionate amount of state funding away from all the other state schools, as Florida did until recently.
So, yeah, I'd EXPECT a flagship state school in a southern state that for most of its history did not admit women or blacks and which siphoned off most of the state funding for over 100 years to be AWESOME.