The proposed CIP regulation required banks to verify the identity of mere signatories. Some banks protested and the final regulations only required banks to perform their CIP processes on a "customer;" i.e. the entity. My opinion is that the current industry standard ignores that shift and requires verified identification of all signatories, regardless of whether it is required by law. (Kaybee is correct, it may be more akin to customer due diligence, but the easiest place to plug it in to the process is in the bank's CIP.)
I've waited to offer this comment until there were over a hundred "views" and anyone who had followed the course you are considering had a chance to weigh in. My observation would be that the absence of any such comments would suggest that most banks are weathering the whining coming from some customers and some CSRs and continuing to obtain and verify information on signatories.
Whether it's required by law or not, it's simply prudent. It's far easier to steal the identity of a corporation than it is that of a person; it's identifying the signatories that gives the process some meaning. (Excluding signatories on government entities and publicly traded companies still falls within the "prudent" range, in my opinion.)