From the OFAC website FAQs:
"Who must comply with OFAC regulations?
All U.S. persons must comply with OFAC regulations, including all U.S. citizens and permanent resident aliens regardless of where they are located, all persons and entities within the United States, all U.S. incorporated entities and their foreign branches. In the cases of certain programs, such as those regarding Cuba and North Korea, all foreign subsidiaries owned or controlled by U.S. companies also must comply. Certain programs also require foreign persons in possession of U.S. origin goods to comply. [09-10-02]"
I think you will find that banks take a risk-based approach to how far down the line they check OFAC. Certainly on all primary relationships, but some banks do not check payees and some do. It is risk-based.
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"No problem can withstand the assault of sustained thinking." ~ Voltaire
"Sustained thinking gives me a headache." ~Me