Some of you are going overboard here. Interviews at nearly all schools are granted on a rolling basis, whether their admissions are rolling or non-rolling. Thus the earlier you get your app in, the better your chances at an interview. For rolling admissions schools, the stakes are even higher: the earlier you get the secondary in, the better your chances at an interview, and the earlier you interview, the greater your chances of admission.
If a school can fill its interview schedule up with the applicants it has reviewed before the secondary deadline, then there is nothing unethical about them doing that.
Most schools urge applicants to send in the secondary ASAP. Without looking back over anything I received specifically from NYU, I entered the app cycle knowing that, all else equal, sending in the primaries and secondaries early will yield better results than sending them in late.
SDNers argue all the time about what constitutes a "late" app, but suffice to say, if you don't submit a secondary until right before the so-called deadline, you are very late and your chances at an interview are in all likelihood less than they would have been with a more timely app. Personally, I think that any secondary submitted after September 1 is getting late, and after October 1 is definitely late.
Bottom line: I see nothing unethical about what NYU has done here. Unless you can find some sort of written guarantee from NYU, or any other school for that matter, that all secondaries are given equal treatment no matter when received, or something like that, I think you are wasting your time writing angry emails to the school and raising ethical issues with AAMC.