Please correct me if I am wrong, but I have been told that university admissions offices, whether need blind or not, can see if an applicant is applying for financial aid. If the university is need blind, they may not know the details when they are making admissions decisions, but they can see who is full pay and who is not.
I doubt that universities with massive endowments like Harvard, Yale and Princeton care or pay much attention to this, but you have to wonder if other prestigious need blind universities with much smaller endowments (Harvard’s endowment is roughly 8x that of Brown’s for example) are occasionally influenced by an applicant’s financial aid status.