Yeah I'm pretty sure I understand what you're talking about and as far as I can tell it doesn't really have anything to do with quantum mechanics at all.
Entanglement is "just" the result of the fact that the space of possible states of a combined quantum system isn't the Cartesian product of the state-spaces of the subsystems that make it up.
If I have two classical systems, one of which has state-space {A, B} (i.e. the first system is either in state A or state B) and the other has state-space {0,1,2} (i.e. the second system is either in state 0, 1 or 2) then the system I get from combining them has 6 possible states {(A,0), (A,1), (A,2),(B,0), (B,1), (B,2)}.
Thats not how quantum state-spaces combine, they combine with the tensor product, rather than the Cartesian product, so the state-space of the combined system is much richer than what you'd get if you try to use the classical "Cartesian product" rule to combine them.
Entanglement is "just" the result of the fact that the space of possible states of a combined quantum system isn't the Cartesian product of the state-spaces of the subsystems that make it up.
If I have two classical systems, one of which has state-space {A, B} (i.e. the first system is either in state A or state B) and the other has state-space {0,1,2} (i.e. the second system is either in state 0, 1 or 2) then the system I get from combining them has 6 possible states {(A,0), (A,1), (A,2),(B,0), (B,1), (B,2)}.
Thats not how quantum state-spaces combine, they combine with the tensor product, rather than the Cartesian product, so the state-space of the combined system is much richer than what you'd get if you try to use the classical "Cartesian product" rule to combine them.