If the parents are not US Residents, yes (I think the one box will automatically check).  The $500 credit does not apply unless the dependent is a US Citizen, US National, or US Resident.

However, you stated the customer is "claiming" he pays for all of his parents' expenses.  Maybe I'm misinterpreting it, but I get the idea that you have doubts about it.  If you have doubts, but sure to get as much documentation as possible to prove their claim.