So, what's the difference between him paying MY mortgage for me or his paying rent to me while I write the mortgage check? The house is STILL in my name along with its tax records and therefore I own it. He's effectively renting it from me. Yes, it's quite possible to be a tenant in one place and landlord in another.
Keep in mind, though... this also puts me in a position to sell the house right out from under him, put him in the streets and walk away holding every penny. So, there's really no suckering going on.