Sometimes, banks are just confused about why they require something to begin with.
You ask for a copy of the DBA registration to verify that the customer has the legal right to use the name on the account title and the payee line on the check. You do that because you are going to guarantee every endorsement using that name. If you identified the individual who is using his or her own name, you already know whose endorsement you are guaranteeing and are assured of his or her right to use that name.
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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.