Here is my anecdotal argument against that point.
One of my sons was a competitive applicant for highly selective universities. He just graduated last May from a US News Top 10 school. We lived in Florida, he attended high school in Florida, so he also applied to Florida universities. He was accepted by UF and their Honors Program. He was accepted FSU but rejected by their Honors Program. We got the FSU decision first and it scared the heck out of all of us, wondering if he would even be accepted by UF.