If you are opening a bank account, a background check is not required. The only thing the US bank would do is to check the person against the various lists they have such as OFAC, SDN, etc.
If a background check is required for some other purpose they might outsource this task or contact a specific background check company in the country from which the person came from.
If a background check is required for some other purpose they might outsource this task or contact a specific background check company in the country from which the person came from.