In Something Positive, Aubrey describes a variation of the trope when, asked why she's never been arrested, she responds that "the key is to commit crimes so confusing that police feel too stupid to even write a crime report about them."
The Adventures of Dr. McNinja: In one of the earliest examples, vigilante paleontologists discover living dinosaurs, so they dress as gunslinger banditos while riding velociraptors, thus preventing the authorities from doing anything about them because they refuse to believe the reports.
"These are my antennas, because clearly I am a robot. Also, robots never lie."
Erfworld's Parson seems to understand that taking Refuge in Audacity is the best way to skirt the rules. Uncroaking a dormant volcano is so audacious that it shouldn't be possible, and nobody has even considered trying it before, which means when Parson pulls it off successfully, it catches everyone so far off guard that he turns the tide of a war.
ThisTouhou fancomic. Nazrin shows up and thanks a pair of (low-power) gods for the food she just stole and ate and calmly walks off. The victims are too stunned to respond.