Now, is any of this true?

Not really, since keys work by shorting the circuit. That's why pressing multiple keys at once on your keyboard doesn't cause it to blow up. It would just assume the button with the shortest circuit was pressed, and ignore the rest.

It might cause weird things to happen with a mechanical or electromechanical calculator, since there were physical mechanisms engaged and disnegaged for each function, and might break/jam those, but not an electronic, and especially not a transistorised one.

It's more likely that hitting them all confused the CPU, or dropped the voltage down enough that it reset, just in case something strange happened, or to try and fix any bug that might have caused it to register all the buttons being pressed.