Tony, I think he meant leaving the battery in when using AC power for long periods would result in shortened battery life. I do not think it is related to the sequence of AC, battery in or out, or removing AC or battery while the computer is on.

I have experienced short battery life on Li-ion batteries in a Toshiba Libretto and a Dell Inspiron which are normally used on AC power. I now use them with the batteries slipped out while on AC. This has resulted in much increased battery life although I have gone thru several batteries on my way to acquiring wisdom! Good luck.

Michael