Whether he owns the house or not is irrelevant and none of her business.
If he wants her to pay rent to live in his house under false pretenses that's his choice.
Again he owes her nothing.
I disagree, successful relationships are largely built on trust and honesty. If you cannot be honest about your homeownership than you should not be letting that individual live in your home.
Co-habitation should be a stepping stone to a long lasting, serious relationship. A serious relationship should value building together as well as helping eachother.
Lying and believing it’s okay goes against those values, doesn’t make sense for a healthy relationship.
At the end of the day no one is forcing you to do anything sure, but in terms of what I believe to represent a healthy and successful relationship, all that is a no. Man or woman.