Throughout my career as an air traffic controller and a lifetime pilot, this has been an issue. Same discussion...different frequency band and users. I don't think I've gone a year in my aviation career without hearing a stuck mic.
The chance of having a second radio is the only explanation for the transmission that makes sense to me. Fortunately, airplanes typically move fast enough that the problem eventually fades away.
In FAA Flight Check, we'd get called in to find illegal broadcasts or interference. In some cases of frequency interference, such as pirate radio stations or illegal transmitters, we'd fly around the area reported as problematic with receivers and homing devices that allowed us to get a fix on the transmitter. Eventually, we'd get enough hits to pinpoint a neighborhood. Then the white van was dispatched to find the perps. It was a fun game of cat and mouse. Nowadays, the USCG should be able to triangulate the position from the VHF broadcast on Ch 16.