Owner Landlord looking for potential renter Credit report

[Dax Gurr]

I have a rental that is kind of unique so it is a little hard to rent.  I have had what I thought was a great potential renter complete the application.  The problem is both the husband and wife have terrible credit ( in the 530's).  I get all the information on the application verified before I run credit.  I hate charging people if I have no intention of renting to them. I called the current landlord and she says they have paid on time for 6 years and is sad to see them move.  He is retired military and has a pension.  When I ask about it they said it was a family member who committed identity theft.  Is there a way to verify that?  Should I ask for a higher deposit? I guess my big issue I don't know how to read credit reports. Any thoughts would be greatly appreciated.  

[Dax Gurr]

Thanks @Account Closed and @Nathan Gesner

I like your idea of running a background check prior to looking at someone.  I think sometimes I try to accomidate more than I should.