It's not about getting correlated outcomes when the measurements are made, that would be unsurprising. It's that the correlations (or more precisely, the distri

It's not about getting correlated outcomes when the measurements are made, that would be unsurprising. It's that the correlations (or more precisely, the distributions) of the outcomes conditioned on seemingly random measurement choices suggest that the outcomes are not from independent measurements. Now there are several ways you can interpret that: 1) the measurement choice at one site is superluminously conveyed to the other site and causes an effect; 2) the measurement choices are not independent and random despite the best attempts of the experimenters; 3) the wavefunction over the two sites is physically real and both measurement choices are necessary to sample it.