Fujitsu lifebook battery lifespan

So my classmate tells me that charging a fujitsu notebook battery while it's at full power will reduce its lifespan. He personally takes the battery out and runs it solely on the charger because of this. (also puts him at great risk of losing data because if someone steps on the charger and he hasn't saved, well.. Instantaneous shutdown) I was wondering if there was any truth to his statement; I did a search on google and I couldn't find any sources stating that plugging the charger into your notebook computer while your battery is at full power reduces battery lifespan. Does anyone know if this is true?

If it helps any, the label on the back of my battery case says 'li-ion 20' so I presume it is a lithium ion battery.