I think their problem is considering that the labs L1 and L2 are isolated quantum systems because there is obvious entanglement through the state S. In the seq

I think their problem is considering that the labs L1 and L2 are isolated quantum systems because there is obvious entanglement through the state S. In the sequence of events that they present at T1 the observer in L1 prepares S, transfers it to L2, and knowing the current state of L2 predicts what the observer outside L2 will measure later assuming that L2 is left unperturbed (the actions of the internal observer do not affect the system). But this prediction is invalid because the protocol specifies that before the last observer enters the scene at T4 the system L1/L2 will be perturbed by another external observer (the observer outside L1 when he does his thing at T3, as you said he's effectively measuring Z).