Count me as a skeptic, but I believe some need blind schools have a high degree of understanding of a given applicant’s financial status. The data, reports and predictive models they are using get very granular at the zip code level (as well as other ways).
In our experience with athletic recruiting, every coach (ones which we had more than cursory conversations with), asked us if we would be applying for financial aid. This was true whether the school was need aware or need blind. When we answered that we would not be applying for fin aid, every single coach said something along the lines of ‘that’s good’.
Based on this info (why would a coach from a need blind D3 school with no merit aid need to know if we were applying for aid?), along with the other data points they analyze, I expect that some need blind LACs, when admitting say 250 students in the ED round, have a very, very good understanding of who doesn’t need aid, who does, and how much. Going into the RD round, they wouldn’t have the data for the 60-80 tagged athletes and Posse applicants, but they still have all the other data points they are gathering to help balance the class and stay within budget with regard to financial aid.