So say you have 5 people apply and give you applications and checks for app fees. You pick the best one that meets your standards, run their background/credit check and find out they lied. No app fee returned - cash that check for your wasted time and the cost to run the background/credit checks. Based on their application they DID qualify to live there, but when you verified it and they had lied/misrepresented they DIDN'T. The form states that in this case they get no refund. They are out the money for lying. Had they been truthful they would never had the background/credit checks done and would have gotten their check back in the mail.
Had they been telling the truth, their background/credit check would have backed that up and they'd now be getting the rental. Then you would mail back the uncashed checks to everyone else that you collected them from, because their apps were never processed and their background/credit checks were never done.
Here's what I do. I'm very clear with people that they need decent credit and a CLEAN background check. I have it on my website and I tell it to them before they even apply. I don't collect an app fee, I just review applications and if they qualify based on that info I'll send them the link through SmartMove and let them pay the $40 fee there. I get the info I need emailed to me and we are done. They can't ask me for the money back because they didn't pay me. Had they been honest, they wouldn't be out the $40.
I would decline them based on his criminal history. If they question it just tell them that that is why you ask for this information on the application and if he had been forthcoming with that information at that time that they would have been disqualified immediately based on that information and gotten their app fee check returned.