This was frighteningly familiar to read. I grew up the child of a gaslighting narcissist father and this is textbook:
1. Downplay or deny the concerns. Accuse the person pushing back of overreacting. Insist on speaking directly yo the accuser. Do not do this in writing. Deniability is paramount.
2. Attack the person. Shake their own faith in themselves if you can, but at least discredit them to anyone else who might find out about their complaint. Any perceived weakness is fair game.
3. Go on at length defending yourself, as publicly as possible. Ignore the fact that you make no sense. Sense-making is not your job. Volume is.
4. If you still have not won, overreact in the extreme. Misconstrue every conversation. Take full advantage of your earlier refusal to commit anything to writing. Use this to emphasize your original downplaying of the issue. Further discredit the person by making it seem as though this were not just the appropriate response to their complaint, but the only response possible.
5. Never, ever, under any circumstances, explain your overreaction.
I can smell this pattern from a mile away. It's incredibly hard not to become defensive against it and reply from your own agitation.
The only way to win is not to play. Do not engage the narcissist directly. There is no rationality there. You absolutely cannot win at their game. Under no circumstance should you agree to communicate in a way that is not recorded, but better yet, do not communicate at all.
Respond only to inquiries by sane people. Your refusal to engage the narcissist on their terms will make them hopping mad. Let them be mad. Sane people will see it. Even then, respond only in recorded ways.
No good comes from a leader like this.