What is the ruling on Muslims in America requesting food stamps designated for the poor, while concealing information about their bank accounts to obtain them? And is their statement that this is not unlawful because they are not taking from an Islamic country correct?

It is not permissible to reside in non-Muslim lands except with a legitimate excuse and under specific Sharia (definition) conditions. It is also not permissible for those who are not entitled to take coupons, whether the issuing authority is a Muslim or a non-Muslim state, because this falls under the ruling of lying and unlawfully consuming people's wealth. Allah the Almighty has condemned those who beg from people while not in need, and praised the chaste who do not beg persistently from people. Furthermore, Muslims must abstain from such actions that tarnish their religion.