Many years ago, I worked for an Edge Act Bank in the Miami area (only catered to foreign customers). One loan officer made a CD secured loan for $2,000,000, secured by 20 x $100,000 CD's and 2 x $250,000 CD's, all of which were endorsed to the bank, and in our collateral vault. He was therefore over-securing the loan by a half-million dollars. After a few weeks, the LO was getting a bit nervous on the amount and asked an attorney for an opinion if the loan was iron-clad.
The attorney came back with a 7 page letter indicating those cases where the bank might not be secured. Some issues included cash not declared when entering the US, tax liens, and a whole litany of similar things, etc. While those situations are unlikely, a credit report may help. Some banks required it for all loans - others excluded loans amply and entirely secured by bank deposits. Make sure that it is in policy, documented why it is there, and like Richard mentioned, done the same in all cases.
Integrity. With it, nothing else matters. Without it, nothing else matters.