Came across this the other day. I've noticed with my car running and Powerlab8, the charger triggers a safety function that occurs when the voltage functions are beyond the designer's safe levels. A some amount of fluctuations can be absorbed by the chargers input capacitor. But large amounts, over time can be hard on the capacitor.
In practice, chargers need a fairly constant input voltage. This does not mean ripple-free, but free of voltage fluctuations. If the input voltage of the charger suddenly rises or falls, the output current does the same, as the charger's electronics need some time to compensate and readjust. The output current can fluctuate quite a lot, for example 4 times as much when the input voltage rises by 1V. This is also the reason why one should not charge from a car with the engine running. It has happened that chargers were destroyed by the fluctuations.