I thought it was a myth too, so when I got my first cell phone, I left it plugged whenever I was home, even when I had used it so little that it was still showing full charge. After a time, however, its battery started to get "fat".

I bought a new battery, and since then only plugged the charger when the phone was no longer showing full charge. That battery still works, and is still as "thin" as it was when bought.