Assumption of molecular chaos

Assumption of molecular chaos in statistical mechanics states that the incoming velocities of two colliding particles are uncorrelated.

Now, since it introduces a direction of time, this hypothesis obviously could not be derived from the classical equations of motion for particles (F=ma and etc., or their more mathematically elaborated counterparts).

My question is: are there any logical arguments showing the above hypothesis is compatible with (i.e. does not imply something strongly contradicting) the Newtonian equations of motion, other than that it manages to provide predictions agreeing with experiments?

My own thoughts on this: since it breaks the time-reversal symmetry of the classical model, molecular chaos is indeed incompatible with the classical equations of motion. But this raises the further question of why, then, are we allowed to use classical mechanics everywhere else in statistical mechanics.