LOL! Thanks for making my afternoon. Cracked me up.
Here's my two cents...this guy would have creeped me out too, and I'm a guy. Agree that the Air rep was totally inept. You don't ever owe ANYONE an explanation for anything when it comes to inviting someone into your home. And, you certainly don't need to lie. In fact in this example, the Air rep's guidance just made things worse for you. Here's how I handle red flag people:
Press DECLINE with the following: "Thank you so much for your interest. We are unable to accommodate you. Best of luck with your travels."
Do nothing else after that. You don't have to say why. You don't have to make things up. Just ignore. This kind of person tends to be very socially needy and will go away fairly quickly once he learns he's not getting any attention from you.
Although I have never had anyone continue to harass me after following this procedure, if I ever did I would just alert Air in writing to flag this person as someone they need to deal with.