I strongly agree with McFly and Happy - there is no requirement to provide full information about the subjects of a SAR. Off the top of my head, here are some things you can do in your discussions with the examiners:
1) Ask them for a citation on this, which they won't be able to provide.
2) Remind them of the FIN-2012-A002 which talks about how SAR disclosure by directors has been a problem in the past, and then explain how your process mitigates the risk of SAR disclosure. Fin-2012-A002 can be found here:
https://www.fincen.gov/resources/advisories/fincen-advisory-fin-2012-a002 3) Explain that providing subject information can be problematic if a director is ever the subject of a SAR. Here is an article were I explain the challenges with this:
https://www.compliancecohort.com/blog/board-reporting-on-director 4) Now, I'm wondering if the examiners are concerned from a Safety & Soundness perspective in that a director approving a loan should know if the bank has other concerns, such as knowledge or suspicion of illegal activity. In that case, you can set up a SAR committee that involves your President who will be at board meetings and could bring up such information if the need ever came up. Here is a short video where I discuss the safety & soundness concern of providing subject information to directors:
https://www.compliancecohort.com/blog/reporting-sars-to-the-board-of-directors 5) If all else fails and they still recommend this - or worse, include it in the report - I would work this up the chain of command before I agree to implement this frivolous recommendation.