Naturally, I figured it would be an arrest.

I saw hundreds of knuckleheads in Michigan protesting and no one getting arrested, so I'm guessing you wouldn't get arrested providing a needed appliance to your tenants. 

But if he's not on the lease, he has no obligation to pay rent.If he looks shady (evictions, arrests, criminal), then just tell her flat out to get him out immediately. 

She came to my apartment with him in tow (to be honest, he was pretty meek - no doubt didn't want to go back to prison and was probably on probation) banging on my apartment door (I was resident manager and didn't have a separate office) and yelling that I needed to rent to her brother or I'd be sorry.I called the cops who let her know she could be arrested for harassment and she better knock it off.Sheesh, I wouldn't be surprised if the brother actually took the fall for something she did.I did have a couple of other applicants who I turned down who behaved the same way, coming onto the property or telling me over the phone that I needed to give them the owner's information, coming onto the property and basically stalking me demanding that I rent to them. 

They're not setting you up for a lawsuit or an arrest.

I think he may have been arrested or something..

If he tries to enter, you can have him arrested for breaking and entering.

I check my county clerk of court for evictions, arrests and lawsuits.  

A year or so later they were arrested for some elaborate multi million dollar Ponzi scheme!

And if you dont actually do that, as @Matthew Paul said, the Baltimore States Attorney was just arrested and convicted of mortgage fraud for not meeting occupancy requirements of a loan for a property on a short term rental.