No way! My DH would have threatened to call the police if they didn't leave too. Good on your DH for not letting them in. After the experiences we've had with some not so friendly rental agents, my attitude is stuff em. Know your rights and stick to it. We had them turn up without notice once. Unfortunately we weren't home to not let them in. Not happy campers here. I tell anyone who asks never to rent through that agency (as tenant or landlord) if they can avoid it.

I'd also be rather concerned about the structural integrity of the house given the response in point 4. Unfortunately I think it is within their rights to say no to that one without giving a reason. The reason they gave is rather stupid IMO.