The explanation you're supposing for the "spooky action at a distance" is called a hidden variable theory, and as others have said, this explanation has been disproven. You might be wondering how, and I'll tell you the scenario (adapted from The Elegant Universe) that helped me understand.

Imagine you and I each have a device: a small box with one openable window on the top, one on the front, and one on the back. When one of these windows is opened, it shows either white or black. Further, I tell you that these boxes are entangled: if we both open the same window, the same color will be displayed on both boxes. This only works for the first window opened and only if we both open the same window: if a second window is opened or if we open two different windows, the colors shown will no longer be correlated in any way.

I actually have many of these pairs of boxes, each pair numbered uniquely to identify its matching twin, and we run the experiment for an arbitrarily large number of them until you're satisfied that my claim holds true. You see nothing special about these boxes and argue that they're simply preprogrammed from the factory to display a set of colors the first time a window is opened (for example, BWB or WWB). I counter that entanglement is special and the boxes are not preprogrammed from the factory. In fact, they decide at random which color to show right at the moment one of the boxes' windows is opened!

My claim seems crazy and at first glance possibly even unprovable! But it turns out with a bit of cleverness we can test this.

We take an arbitrarily large number of boxes and begin independently opening their windows at random (without consulting or coordinating with each other when deciding which window to open), recording box numbers, window choices, and the resulting colors. When finished, we compare notes. Sure enough, when we both open the same window on entangled boxes, the colors match as expected. Upon a closer look at the data, we discover something surprising. Ignoring which window we opened, each pair of entangled boxes showed the same color exactly 50% of the time. How is this surprising? A little bit of probabilistic analysis conclusively demonstrates that such a result is fundamentally incompatible with any hidden variable theory.

Assume for the sake of argument that the boxes are preprogrammed. The only possible programming for each box is some form of XXX or XXY. Consider: if both boxes are programmed WWW (or BBB) and we both open a window at random, it will show the same color 100% of the time. If both are programmed WWB (or BWB, or BWW, or any equivalent variant), 2/3 of the time there's a 2/3 chance of displaying the same color when choosing windows at random and 1/3rd of the time there's a 1/3 chance. Combined, whenever the colors are in an XXY configuration, there's a 5/9 chance of showing the same color when windows are chosen at random. Note that in both scenarios the odds of seeing the same color from randomly-chosen windows are greater than 50%! Assuming the preprogrammed colors are chosen at random, some form of XXX will be chosen 2/8 of the time and XXY will be chosen 6/8 of the time, we see that the total odds of seeing the same color if the boxes were preprogrammed should be 2/8 * 100% + 6/8 * 5/9 = 2/3. In theory, our data should have shown a 66% agreement in color, but our experiment consistently shows colors matching 50% of the time.

A hidden variable theory—any hidden variable theory—runs into this probabilistic hurdle.