...this is a question on our new account application
It is a question on our application.
I encourage you to simply follow your prior respondents' lead: Ask every new customer in which country are they a citizen.
There are enough permutations in regard to their status in the U.S. and taxpayer identification numbers to make things complicated, but you need a clear, unequivocal answer to this question. It's due diligence at the fundamental level and, as Rosie illustrates, figuring it out after the fact is labor intensive and, perhaps, imprecise. For example, having an SSN tells you nothing; they can be obtained by citizens, resident aliens, and, under some circumstances, non resident aliens.