LOAs are NOT guaranteed admission. They are guaranteed an appointment IF they are medically qualified, pass their CFA AND obtain a nom.
USNA has ~1200 slots in the incoming class. The number of appointments offered is tied to "realization" -- i.e., the number of acceptances they expect based on the number of offers they make.
I stand corrected. It is assumed that you are going to be medically qualified, pass The CFA and obtain a nom. With out those you cant get in anyway.