USC meets need according to its own special definition of “need.” Your definition of “need,” and even your EFC of 0, have no bearing on USC’s definition. USC’s packages almost always include loans and some family contribution even if the EFC is zero. This happens every year, not just with USC but with many other “we meet full need” colleges. There’s really just a tiny few who will typically give a full ride to a “0 EFC.”
A “0 EFC” student can’t be so picky. Take one of your full ride choices. There is a really, really long list of students who would love to have those choices. Congratulations on your admissions!