What they want is total control over your bank account, simple lawful bully boy tactics where you take on ALL of the resulting risk. Imagine letting your local shark or used car salesman free reign to choose how much/when they can access. You are probably dealing with a structured lawful business designed entirely in the event of any cash flow problems/fraud to wind it up at no loss to those higher in the food chain. The way property is heading the future will be interesting.
Call your local tenancy advocacy group for your true rights, no one within the rental industry will let you know the truth, the character set needed to satisfy the rental industry disallows this.
We had the same problem a while back and although they blustered we crushed them in the end...no personal character/expensive garbage is at the root of the rental industry so it's usually quite easy to do.
Do not give one single inch of ground....if it is not stated explicitly within the standard rental agreement the existing conditions override.....actually you could using their very same mentality charge for same such access....worth considering....as a confuser at a least.
Seek free legal advice in your state to save being just another dumb sheeple...it's what they rely on.
