OFAC compliance is risk based; there is no circumstance where your bank is required to check the list.
OFAC guidance indicates that if the SDN owns more than half of the entity then the entity is also to be treated as an SDN. Checking the signatories and principals simply indicates your level of risk aversion.
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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.