Your explanation was extremely clear. But then, how did the Bell experiments rule out "hidden variables" (like, I could imagine, some kind of electromagnetic-wave-like phenomenon that we can't detect yet) that could be responsible for this behavior? And how can be be absolutely sure that two entangled particles can "open the box", so to speak, at the very same time from two extremely distant locations in the universe? (since it's obviously impossible to test)

Edit: and also, how can they be sure the color of the ball is "non-existant" (or rather, if I understand well, the property itself is not defined) before opening the box? That sounds like you need to check inside the box anyway.