It's like you and a friend have a deck of cards.
You each take a card from the deck, and then travel a million miles away.
Then, at the crack of noon (synchronized to GST, of course), you both look at your cards.
Your card is the 3 of Clubs.
You travel back to meet your friend, and discover that his card (which he measured at noon, just like you) was the 7 of Diamonds.
You repeat this experiment a gazillion times and are amazed!! No matter how many times you run it, you and your friend never get the same card!!!
It's as if the cards are sending spooky signals to each other.
And after you double check that you and your friend are both looking only at 1200 GST, you realize that this spooky signal travels faster than the speed of light (since the it takes no time to "travel" a million miles).
It's like magic, eh?
Not really. The fact there is one of each card means it's impossible for you and your friend to have the same card. No magical spooky signals are being sent.
(I think the quantum mechanical case is analogous to this contrived example. The difference in real quantum mechanics it that you really don't know what card you have until you look at it. However, that doesn't mean that your card is sending a faster-than-light spooky signal to tell the other card what to be. And you certainly can't use it for signalling or anything useful.)
((Reposted to main thread with some slight edits, in case people find this comment useful or interesting.))