I'm pretty sure that's not true.
Some battery/charger combinations rely on the battery's BMS to stop charging once each cell group reaches 4.2 volts (54.6 volts for a 48 volt battery.)
My Das-Kit charger goes from red to green when charging is finished, but it still puts out 54.6 volts while the light is green.
With my new battery and charger from
@Jenny Mao, the charger shuts off completely after the charge is complete.
The Bosch charger may very well shut off as well?
If there is no specific warning in the owners manual about unplugging the charger after the the light goes off, then it probably does shut right off.