Why can't OverbearingCompany send a letter stating something like we notice your logo or other IP is similar to ours. We recognize that we are in different businesses, and so we choose not to pursue this matter at this time, but we reserve the right to pursue any legal remedy at any time in the future that we determine your material to be infringing on ours.
That would demonstrate that OverbearingCompany is practicing all due care, yet doesn't waste OverbearingCompany's time and avoids potential destruction of SmallUnderdog.
As things are, the mere existence of large, overbearing companies causes accidental and sometimes catastrophic injury to the small and cuddlies of the world. Is that really what IP lawyers dreamed of doing when they were kids?