Some context ...
You can interpret QM predictions of separated measurements on entangle systems like this in two ways:
(a) You insist that any quantum uncertainty might be a result of ``hidden variables'', and so follow the rules of classical (ordinary) probability. This requires the two parts of the experiment to be able to signal to each other instantaneously: i.e. the so-called ``spooky action at a distance''
(b) You prefer to retain the speed-of-light speed limit for cause and effect, but at the cost of disallowing hidden variable (standard probabilistic) models, and thus need to describe things using complex probability amplitudes - i.e. quantum probability.
Most physicists prefer to choose (b), because they prefer to retain causality over a model respecting classical probability theory.
Nevertheless, it is valuable to test both ideas. As I understand it, here the authors' have said: if we choose a hidden variable interpretation (choice (a)), what is the experimental bound on the speed of information transfer?
This doesn't mean that the interpretation (a) is the ``true'' interpretation. It doesn't even mean that the authors necessarily prefer (a) over (b). But it does tell us something about how things (might) work /if/ (a) were the best interpretation.