That's the common explanation, but its apparently wrong. There is not a fixed state of each 'quarter' in each 'box'. They are truly not determined until one is resolved; then the other is resolved simultaneously. Still, not communication.
Thinking about this makes it clear how communication is impossible. You will always get both answers - for different values of "you".
Relativity of course makes a hash of that.
Still it's as close as you'll get with a classical analogy, and if you only have access to a fixed basis is entirely correct. Expanding beyond the classical explanation is only truly necessary when you start measuring in different bases.
Isn't that unknowable? And aren't both situations (fixed vs undetermined) effectively the same from an observer's point of view?