Isn't this distinction exactly what the article is about? By saying ahead of time, "one ball is red, the other is blue", you're describing a hidden-variables theory of entanglement. It may be unknowable (before measurement) which color the ball in your left hand is, but it has a color.
But Bell's theorem provides a very measureable counterexample to this type of explanation of entanglement. Sure, in the article they talk about electron spins instead of ball colors, but the analogy is that there isn't a well defined "color of the ball" before it's measured.
Of course, the analogy breaks down a bit: electron spin can be measured in multiple axes with somewhat complicated interactions.
But Bell's theorem provides a very measureable counterexample to this type of explanation of entanglement. Sure, in the article they talk about electron spins instead of ball colors, but the analogy is that there isn't a well defined "color of the ball" before it's measured.
Of course, the analogy breaks down a bit: electron spin can be measured in multiple axes with somewhat complicated interactions.