Looking dumb is oodles better than lying.
The risk of false accusations is one of those risks that accompany success and senior leadership positions. The only way to insure yourself against this risk is to be publicly, privately and deliberately squeaky clean.
Integrity ensures you solve and do not ignore real problems. It acts as a forcing function for needed improvements.
Lack of integrity on the part of an individual is often a key indicator of a deeper problem in the organization of unit.
No matter what you have heard, personal integrity is in itself an excellent armament. There is always room at the top for an honest man.
A single lie can deed your soul to the devil for eternity.
From my Shipmate and occasional mentor - Rear Admiral Dave Oliver Jr.