It is not a problem to open a bank account, and anyone can do that. Some bank clerks will make faces to non-american clients, but that's their problem. They will probably have to show two different photo id's (passport and another ID) each. In some banks, a credit card on their name can be treated as a second ID, but not everywhere.
Check my blog (in the signature) for practical advices on how to choose the right bank for you. Make sure they don't have to pay any fees.
