Landlords or brokers who make statements like these are not aware of housing laws enforced by NYC Human Rights Commission. Make sure to take down their name and information to report their misconduct.
This is a subtle attempt to discriminate specific applicants, although statements like these can sometimes be difficult to act on. If you are applying through Craigslist or another housing site, and continue to see units listed in the building you have applied to, despite being told there is no available space, make a note and report it.
This is a another subtle method used by landlords that discriminates based on income. Often times they will use this as an excuse to end the conversation with no intention of following up. Make sure to record and report situations like this, especially if you have tried multiple times to get back in touch.
Besides particular public housing units, no buildings in New York City with 6 or more units get to decide how their tenants will pay rent. Double check that the building meets theses standards, and follow up with the landlord or whomever you spoke with.
This is an illegal tactic used frequently in the housing market. Many times, landlords will request that an applicant's income is over 40x the market rent. Anything above 40x immediately eliminates all voucher holders from applying. If you see a number above 40x the rent being advertised, report it!
Statements like this are examples of landlords who treat tenants or applicants differently based on their income, a clear form of discrimination. Never pay additional fees on rent without making sure you understand the cirumstances and they are lawful charges.