"No superluminal signalling" is a law of relativity.  Quantum correlations obey the letter of this law, but not its spirit:  on the contrary, nonlocal quantum correlations seem to require superluminal signalling (that is inaccessible to us).  Here we show how quantum entanglement could arise from global random fluctuations that are, by construction, non-signalling.  Indeed, we derive quantum mechanics and classical statistical mechanics in parallel derivations from axioms that include conservation of average energy and probability current, and - only for quantum mechanics - global random fluctuations accompanied by an epistemic constraint.