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.

I love that you bring a great technical and insightful answer and then just leave with that my calculator is probably posessed.

I think this is actually still an issue. On PCs the space bar + up + left arrow keys conflicts on some keyboards. Try it: open Notepad, press two arrow keys and then space. Most of them works but if you hold up and left, it will not make a space.

This is annoying in racing games, when you want to accelerate, turn left and use the hand brake at the same time.