If the charger is properly designed, it's going to do the same thing as when the phone is charging while off. The rollercoaster is much shallower because the battery is only doing what batteries do - slowly discharging over time.
If the charger trickle-charges, the battery can catch fire. They're not supposed to do that. They're supposed to shut off the juice when the battery's charged. So - if it's properly designed, there would be no difference between taking the battery out or leaving it in.
If it's almost properly designed it will overcharge - the battery will feel warmed up after the full charge point, meaning the metal tubes inside the battery are now starting to deform and that will reduce battery life and quality.
If in doubt, watch it on the charger, when it hits green/whatever for that model, see how the battery feels - leave it an hour and see if it's warmer. If it is, the rep was right, and in that case, remove the battery when fully charged.
I mention this not because I'm wrong about the design thing - but because with a lot of accessories you never know where they'll cut corners to save costs.