Agreed. For an example of station id happening at slightly off times, listen to a live sports broadcast (like baseball). Due to the shorter time between pitches, station id will instead happen between batters, which won’t line up with any given time.
Same thing with hockey, where radio station id will happen when the clock stops.
Either ambient instrumental music (lots of Brian Eno) or any music that I know all the words to (so that my brain doesn’t have to actively process the lyrics).