When my tenant is late with the rent, he tells me he's short on money because his welfare check has been delayed -- and he expects me to wait for the check. I've tried to confirm this with Welfare, but they tell me they can't discuss recipients. But if landlords can get information from employers and prior landlords, why can't we get information from Welfare?
The workers at the public assistance office were right to turn down your request. Welfare recipients have a legal right to privacy about personal finances.
It's a different matter when you contact employers and past landlords to verify information your applicants have given you. As long as your questions are narrowly designed to elicit only relevant information about an applicant's employment or rental history, these sources can answer truthfully without fear of legal liability. However, careful employers and landlords will insist upon getting the applicant's permission, often called a "release," before talking to you.
Even if the check was in fact delayed, you're under no legal duty to wait until it arrives. Your only recourse is the often worky but sure legal process of termination and, if necessary, eviction. If you want to speed things up, terminate the tenancy with the proper notice as soon as the rent is late.