Connections with People High In Admissions (Very Selective College)- Influence?

I want to start this by saying that this thread isn’t about my own situation. One of my cousins, a white female from a wealthy family, has done pretty well for herself at a good public high school. Her stats are all on the lower end of “in range” for Dartmouth, GPA-wise and test score-wise. She really wants to go to Dartmouth, and has all the normal “good” extracurricular activities, has spent a summer volunteering abroad in Africa, etc. but is not really a standout at anything. However, her family is very good friends with someone who apparently is very good friends with someone high on the board of admissions for Dartmouth. The man on the board of admissions said to “let him know” if Dartmouth was truly her first choice and he’d see what he could do and would meet with her. This honestly all really bothers me because again, my cousin is a good student, but there isn’t really all that special and she comes from a world of tutoring and privilege. By the way, she isn’t a legacy or anything like that. But I’m wondering if anyone’s heard any stories about how influential having some sort of connection with someone “high in admissions” is if they’re not a family member or anything like that. Would this push her over the edge to get in if she appeared like just a normal cookie cutter applicant but he put in a decent word for her?

It’s not what you know, but who you know.

In all honesty, no one can say. If she’s otherwise qualified - and she seems to be - this might give her a much-needed boost. In the same way that legacy students, URMs, First-Gens, and relatives of big donors are ascribed a slight advantage, by virtue of her knowing (or knowing someone who knows) an AO, she could too. How close they are and how good an impression she makes on him in addition to how well the rest of the Committee likes her will determine the result.