I hate to say this, but you ARE supposed to remove a LiION battery from a device that is running on AC power. It's bad for a LiION battery to be run fully charged at a high temperature, which is exactly what happens when you leave the battery in while running on AC.
Here's a good link about proper care of LiION batteries. Contrary to popular belief, you DO have to excercise a certain amount of care to prolong lifespan:
How to prolong lithium-based batteries
So, somebody posted something on the web saying the opposite and that automatically makes them right? Battery University.
Well, I can't get hold of my own personal battery expert right now, he's a mod in the Forum as well but I'll have him take a look at that and he will provide a link that I think will have more credibility.