That a school meets full need does not mean it guarantees it or will give it to all students, even most students. You can be the rare bird who got a full need met package, especially if it’s based on FAFSA EFC. There are even some who get more than need met with merit money. There are merit within need scholarships and need within merit.
Very few schools guarantee to meet full need as defined by FAFSA EFC. I hear that UChicago does but have not verified. A small school in PA, Albright also does. Or did.