The coop is not under any obligation to grant you an interview if after reviewing your application package, you do not qualify.
I would suggest you speak to your realtor about your problems.
Even though I have sold and/or listed in many of the co-ops in West New York, NJ, and specialize in working in that "gold coast" area, I must say that my Nassau, NY colleague has the basics down in her first response. I will say, however, that I have never had a problem with proprietary lease, by-laws, last audited financials access when requested for any of my purchasing clients from the relevant management offices of Blvd. East co-ops but, commensurately, I also keep most of that information in pdf form stored on my computer so that I can furnish it to my clients before they make an offer on a co-op property. And yes, the Board of a co-op can refuse to interview an applicant; this would happen if the tendered application did not satisfy their stated approval criteria. Good luck in your search!
Elena Schwartz, ABR(r)
Weichert, Realtors Executive Club 2010
NJAR Circle of Excellence 2008, 2010
(O): 973-779-1900 x 148
(C): 201-600-1612 (best contact number)