So you've come almost full circle!
maybe the government has no bin for "investegated by the FBI for a silly and innocuous reason". but maybe they do, and lying about it slots you into the bin for "lied on their security clearance form".
I have some silly not nearly as interesting infractions and I wrote them out in detail explaining, without any issue in processing background checks. It usually is something that’s asked about in an in person interview at that point.