The school needs to be relatively sure that Junior can pass the boards and graduate in 4 or 5 years. Classes are so small that every student who fails out is magnified when looking at as the proportion of unsuccessful students in a class. (unlike undergrad where it is not uncommon to have 20-40% fail to graduate in 5 years, it is highly unusual to have >5% flunk out or fail to complete the degree in 5 years).
Someone whose relative (parent, grandparent, aunt/uncle) has a history of supporting the school monetarily in a big way is going to get "every consideration" in the admissions process. That can mean that the kid gets an interview when it otherwise would not have been warrented. That means that someone who knows the score might speak up on behalf of the candidate but at the same time, there are those who will speak out against a candidate that is seeing to get an edge based on family connections rather than abilities.
That said, I've been in on a few situations where a candidate whose
LizzyM score was a full 10 points lower than our average (equivalent to a 508 rather than a 518) was admitted over my objections and the student pleasantly surprised me by graduating in 4 years and matching well.