Actually, thinking about that, your not right. Possibly fully, possibly partially.
Mail runs in the background, because the inbox count goes up.
iTunes runs in the background, because I can listen to music while I respond to this.
Wordpress runs in the background, notifying me when someone has liked one of my blogs.
Audio recording runs in the background, I can record a meeting while I am using Pages to type notes.
GPS runs in the background, letting me know when a turn is coming up, even though I have iTunes running.
So, there are apps that continue to run, even though they've been closed.