I also know people, and the people I know happen to be in the USNA Admissions office and those are the people that matter for purposes of the OP's question. I can tell you that a letter from a personal friend -- Navy Captain or otherwise -- is unlikely to make any difference in the application. Now, if that long-time personal friend happened to be the President of the United States, a US Senator, etc., my view might change. Just being honest.
USNA receives about 7,000 COMPLETED applications a year and each of those has 3 required recs, which means 21,000 recs to review. If every one added one or two or three more LORs, it would quickly get out of control. USNA has said over and over again that they don't need or want additional letters unless they speak to some aspect of your application that your teachers and BGO can't adequately cover -- examples are non-school ECAs that are a major part of your life or for those who work such that ECAs aren't really possible, a letter from your employer.
I'm in no way minimizing the achievements of O-6. My father was an O-6 and darn proud of it (as was I). Many, many, many terrific officers and human beings do not attain flag rank. Moreover, having a flag officer write you a rec won't necessarily make a difference. I've even had kids of flag officers receive turndowns.
Parents are correct about many things . . . which is something you realize more and more the older you get. But you also learn they are not right about everything. In this case, their instincts may be correct for other colleges (I can't speak to that) but they are not in alignment with what USNA has said regarding admission to that institution.
Bottom line: If you or your parents want your family friend to write a letter . . . go ahead. It's not worth an argument with your parents. There's no harm in doing it; I'm only saying that it's very unlikely to make a difference in whether or not you receive an appointment.[/QUOTE
I will again emphasize that we do not know what impact or influence the Captain's letter will have or what harm it will do unless the super moderator is on the board or influences the board and is opposed to the letter, otherwise it can't hurt. If it has no impact then so what. In the world of people we always look for commonality. Believe me in this case I'm pushing my point because I am right. Send the Letter. Good Luck to you