It was a hotly debated topic for several decades. Until 1964 we weren't even sure we could ever resolve it, then a fellow named John Bell published a testable theorem showing a divergence between quantum mechanics and the classical explanation you have above (http://en.wikipedia.org/wiki/Bell's_theorem). In 1972, the first successful experiment of this theorem was performed, and incredibly, it showed entanglement is in fact more complicated than can be explained with classical mechanics http://en.wikipedia.org/wiki/Bell_test_experiments. The experiments have been repeated and refined over the years and little by little, the once common theory of local variables is now almost completely dead.