i think, if i recall correctly, this was a standard feature of iTunes match, where if you play a song it stays on the iPhone
t does this because you can no longer sync music from iTunes.
if you play a song from the radio or beats one it should not be on your phone afterwards.
if you play a song from iCloud then it will stay on your phone
in order to remove the music you will have to turn off iTunes music or iTunes match ( now called iTunes music library )
and delete the song, and then turn it back on
i tried testing this post, and playing a single song from iCloud and then turning on airport mode, and it didn't work