IMHO, it would only be a fair lending violation if your underwriters (or others) used the picture IDs to discriminate. According to footnote 49 of the FFIEC BSA exam manual (and the 2004 FAQs to the CIP final rule), you are permitted to make copies of IDs, though you should be "mindful that [your bank] must not improperly use any documents containing a picture of an individual, such as a driver's license, in connection with any aspect of a credit transaction."
This is something that some auditors and examiners have made a fuss about for years, but I have yet to find anything that says you can't keep copies of ID in a loan file - as long as the pictures aren't used in a discriminatory manner. That said, it is my experience that many financial institutions keep IDs separate so they don't have to worry about this potential conversation with auditors/examiners.
Also, I should mention that making copies of military ID is prohibited, so this discussion is really talking about DLs (assuming the applicable state permits such copy).
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Adam Witmer, CRCM
All statements are my opinion, not those of my employer, and should not be taken as legal advice.
www.compliancecohort.com