I agree! TTC, the critical vendors, for the most part will be fairly large with detailed back-up and recovery procedures of their own. By necessity, many will have multiple sites, scattered around the US, and potentially the world. How is a visit to a site (headquarters, underground recovery, secret back-up hot site) supposed to help the bank.
Their management will most likely not even allow someone into their critical areas, and how would a site visit enhance the bank's knowledge, other than to ensure that a building (named or unnamed) is secure. I believe your regulator is well intentioned but totally out of the loop, or misunderstood.
If FDIC insists, volunteer to visit the vendor's Hawaii location during the winter months.
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Integrity. With it, nothing else matters. Without it, nothing else matters.