Originally Posted by feathermerchant
Remember that there is a transformer in the power supply. It just operates at something like 20kHz instead of 60Hz. A transformer can short primary to secondary making for high voltage on the output side.
Have you ever seen this happen? Maybe if you were using a toroidal transformer and you somehow dropped it and was able to scuff the coated wires but I have never had a transformer short from the high side to the low side. Even if it did, having 120v on the output would still be there even if the grounds were connected. Nothing would happen unless you shorted them. All they would do is burn out your charger. The only time it might be a danger to you is if you grabbed both leads and even then I doubt the main fuse would pop unless you had it plugged into a ground fault circuit. Having the ground lifted in one of the units can still cause the scenario you worry about as that side could still do that.
Anyway, it is easier to just do one so it is probably a moot point.