It IS true that as a private seller you must not have any reason to believe that the buyer is not a qualified buyer/owner for the gun, but to my knowledge a private seller has no legal burden to take steps to verify that the buyer is qualified.Legally, on an in-state cash transaction, you are REQUIRED to check their ID and confirm residence within your state.
In other words, if the buyer were to volunteer that he lives in another state the law says you would be legally obligated to terminate the sale but it doesn't require that you ask him where he's from.
Just to be clear I think it's prudent to ask to see an ID, but I don't believe you are legally required to do so.