You are absolutely right: a high side switch is connected to the supply voltage to be switched and switches this to the load, which in turn is connected to GND. If you have several high side switches, as in your case, all GNDs are connected together, so everything is correct in your case.
Ground is called ground because it is a common ground. You would now have to carefully explain to your boss that his view is ... ahem... does not quite correspond to the fact. You might ask him for his opinion on a somewhat simplified but exactly similar scenario, which I have illustrated in the following picture. Does a short circuit occur there if you close both switches?

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