Talk to the owner and ask questions. I am sure they will give you some information to make you feel at ease.
I have never had anyone not believe that I own the home we have. I guess because I have either talked with them in person or answered all thier questions through the email. I ususally have a more personal touch with my guests, maybe that helps.
If you have a nervous or bad feeling about an Owner, then I would listen to your instinct, or contact the site you found the home on and ask them for help.
I know once you talk to the owner of a home you like. You will be more than happy with your decision to rent a home.