Your client's system is not "perfect," but as Great Blue notes, it does not have to be perfect. The revised examination procedures emphasize the importance of the bank's OFAC risk assessment in its decison making. The flaw you note is common in community financial institutions. If they have done a risk assessment that indicates their risk is low, they may be able to defend the imperfection.
However, many of those currently entering the U.S illegally through Mexico are not Mexicans (I forget the acronym). The closer your client is to "the valley," the less likely a that they are "low" risk in terms of OFAC.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.