I don't think it really helps - you're already working in something like a probabilistic formulation. If you want to use a quantum mechanical justification for it then you need to look at some sort of non-unitary evolution.
Besides that, I don't think anybody is really arguing that the correlations are actually lost after a collision, just that it's usually a good approximation to treat them as if they are.
It's lost at Boltzmann's "molecular chaos" or "Stosszahlansatz" step. If f(x1,x2) is the two-particle distribution function giving you (hand-wavingly) the probability that you have particles with position and velocity coordinates x1 and others with coordinates x2, then Boltzmann made the simplification that f(x1,x2) = f(x1) * f(x2), ie throwing away all the correlations between particles. This is where the time-asymmetry comes in: you're saying that after two particles collide, they retain no correlation or memory of what they were doing beforehand.
Besides that, I don't think anybody is really arguing that the correlations are actually lost after a collision, just that it's usually a good approximation to treat them as if they are.