The regulation does exclude government entities from the definition of "customer." That has no bearing here.
You're talking about requiring identification from a "mere signatory" on an account. If that is required, then it is required by your CIP, not the regulation. If you want to alter your CIP to say you do not require identification from signatories if the customer itself is exempt from CIP, you may do so. It may ease their discomfort, but it won't be much of a decision from a banking standpoint - your bank should be able to identify signatories, pure and simple.
While I agree with the practice, it seems a bit paternalistic that your software would "require" the information. You may want to discuss it with the vendor or see if the answer materializes below.
My experience with people who want others to "think outside the box" is not good.
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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.