My wife's iPod may be experiencing something similar, which may be a misunderstanding of how the iPod and the related music functions work.
We have an iHome clock/dock thing that we use to play white noise for our infant son when he's trying to go to sleep -- if we turn on the iPod via the controls on the iHome dock thing, the iPod automatically starts playing music from the playlist that was last accessed.
If we turn on the iPod by sliding the switch, though, selecting the white noise app, THEN turn on the iHome dock thing, all is well.
I believe these two instances (yours and mine) may be related, and they may be due to how the iPod operates in terms of automatic playing of music. Might not be a "bug" after all, but rather a "feature" of how the iPod operates.
Are you specifically stopping iHeartRadio from playing by pressing the "pause" button? Or are you simply quitting the app or locking the iPod in the middle of a stream, such that when the iPod resumes, it thinks you want to resume playing the music?