I'm not sure that's quite the right perspective. It's not a coincidence that entropy increases over time; the increase in entropy seems to be very fundamental to the way physics goes. I prefer the interpretation "physics doesn't care what direction the arrow of time points, but we perceive it as pointing in the direction of increasing entropy". Although that's not totally satisfying either.
The fact that entropy always rises etc, has nothing to do with the statistical concept of entropy itself. It simply is an easier way to express the physics concept that individual atoms spread out their kinetic energy across a large volume.