Do AM radio broadcasters pick frequencies that are picked up as interference on purpose?
Coincidence.  Better amplifiers have a small RF filter on each of the signal inputs to prevent this.  This was a common problem with phono and tape preamp inputs; these have an additional 40 dB or so of gain (nominally) in the signal path.
Your equipment seems to be sensitive to the low end of the AM broadcast band.  The radio company might intentionally try to put all of their stations within a narrow range of frequencies so travelers can find them more easily when outside their normal listening area.