To TRY to make things clear. . .
If you have an LOA and are otherwise qualified (medical, CFA) AND receive a nom from any source, you are guaranteed an appointment.
If you have an LOA and are medically and physically qualified and do NOT get a nom on your own, you probably won't receive an appointment. I have seen cases where USNA will give you a Supe's nom or a nom from some other source, but I've also seen cases (including last year) in which an LOA recipient did not get a nom and did NOT get an appointment.
If you have an LOA but are NOT medically or physically (CFA) qualified, you won't get an appointment regardless of whether or not you have a nom.
If you are Triple Q'ed (no LOA) AND have a nom, you are eligible to compete for an appointment. The majority of those who are Triple Q'ed and have at least one nom will receive an appointment. A sizable minority will not, simply b/c there are more qualified candidates than there are slots.
If you are not Triple Q'ed, you won't get an appointment, even with a nom. If your deficiency is academic, you will automatically be considered for NAPS/Foundation. You do NOT need a nom to be accepted into NAPS/Foundation.
Finally, all offers of appointment are contingent upon remaining medically qualified and basically not doing something really stupid (drugs, drunk driving, etc.).
I hope this helps and doesn't confuse everyone even more.