vs state schools has narrowed in recent years. 10 years ago BYU was significantly higher than UT state schools. UVa and MI are viewed at the top of the state university heap because the entering freshmen have high test scores and GPA.
They also have elite graduate school programs, which, at least in law and business, is a relative strength for BYU. I think there are more kids who can get into the U or USU but can't get into BYU than there are BYU students who could not get into the U or USU. That's better academic standing.
You can add better research programs at the U, USU or many state universities, but that's more a function of money (frequently from the government) than raw academic capability.
BTW, I agree with nearly all of your comments. Having lived most of my life outside of UT, most folks outside of UT have a vaguely better perception of BYU than most state universities. The U to somebody in the east or Midwest or South figures UU is probably a decent state school and not much different than University of Missouri, South Carolina or Oregon or fill in the blank.