Anon,
No, the CIP regulation does not require you to require more than one piece of identification, but the supplementary information accompanying the regulation encouraged it. It also encouraged banks to use a combination of documentary and non documentary verification.
So, on its face, what your competitor is doing is "CIP lite," but it's fine.
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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.