If someone applies to a safety with stats above the curve of regular students that attend, is there a chance that person would actually get rejected to protect the university’s yield? How much does showing interest matter in cases like that?
It seems like you are referring to the “Tufts Syndrome.”
I think it depends on the school, for one, and whether you are an in-state or OOS applicant, for another. Are you asking with specific reference to UNC?
Also, just because a person has “stats above the curve of regular students that attend” does not make a school a “safety.”
Yes, I was referring to UNC-CH, @gandalf78. Haha I hadn’t heard of Tufts Syndrome before.
As for my comment about being above the curve, I’m aware that that isn’t a sure admission, especially once admissions rates plunge below 20%. But for schools like NCSU and the UNCs, I’m fairly confident they will be hesitant to reject someone with standardized test scores that are above the 75th percentile for that school.
I am in-state. Is Tufts Syndrome a common thing? Yikes.
Would anyone else like to weigh in? 
I’m IS for UNC, and I’m wondering if visiting the school matters at all in committee.
We were told on multiple occasions during visits that UNC CH doesn’t track interest.
Our experience has been the same. My S did not visit until after accepted, and he received several opportunities with his acceptance so it doesn’t appear demonstrated interest was much of a factor.