I think it depends largely on where you live. There’s a reason it’s called the “California Stop.” And arpund Boston, the shoulder is a completely additional, auxiliary lane, which so. many. people. use.
There’s a funny video where a group of people got on the Atlanta 285 loop, spread out across all lanes, and did the speed limit for a few miles. They had a camera set up on an overpass to watch the procession come around a curve. They say they did it to show how stupid the speed limit on the loop was, and I’m sure it was infuriating for the miles of cars backed up behind them, but… yeah. It showed few people there obeyed the speed limit. I don’t know if this is the original; I don’t remember it being edited by a spastic gerbil, but that’s what I could find before I lost interest.
Getting a ticket for going 3 over is silly. That part does seem contrived, and if contested OP could easily get that thrown out. I suspect either OP was being a douche in some other way, and the cop put something down to harrass them, or they dropped a “0” in the retelling.