"You will most likely not be offered an interview for Presidential/Trustee scholarships from USC if you let them know in your application that you are a NMSF. This way you may actually get admitted. "
this is pure conjecture on your part[ colored no doubt by disappointment]
"Most of the NMSF applied are rejected in the end. "
just as they are at individual Ivys, S, C, MIT and many other top colleges with acceptance rates lower than 20%. There is no guarantee of admission at USC for NMF’s.
Getting a high score on a test taken during a students Jr year does not make it MUCH more likely that USC, or ANY highly selective college which evaluates student applicants holistically, will accept them.
Being a NMF is one aspect of a students application- it is not a deciding factor- not even close.