Best Public Universities in the US

Partly, people tend to associate prestige with selectivity factors. In the examples of the schools you named, they vary when compared across colleges nationally from about 37th for UCB – through 42nd for UM, 56th for UVa and 74th for UCLA – to 88th for UNC, at least when considered by narrow measures at the time of this analysis:

https://amp.businessinsider.com/the-610-smartest-colleges-in-america-2015-9

Since this seems to comport with what you’ve heard, the perception of UNC may arise from an objective basis.