This same scenario came up before except the renter did not have the money to pay the rent and then justified not paying rent because the landlord was rent skimming.
I don’t see how the relationship between the bank and the landlord have anything to do with the relationship between landlord and the tenant. You contracted for a place to live and you have a place to live.
Now if you have a down payment and feel that you could potentially lose that, you might mitigate that loss by withholding a month payment. I guess I am with jonnycsd. Seems that all you want is a cut of the action at the banks expense.
If you are going to set up a trust and are willing to turn the rent over to the bank then I will ammend my statement.