I wouldn't think it's related because the very short, 50ms pulse of pink noise has to be precisely timed with the peaks of your existing brain waves to give those waves an extra push. Similiar sounds in nature would occur at random times and antagonise your brain waves just as often as it helped. Imagine trying to push a kid on a swing at random times. They would end up kinda vibrating and not really swinging at all.

On the other hand, perhaps the random times it helps is very beneficial, and the random times it hinders are more neutral, yielding a net benefit.

Still, it would seem very odd that your brain is perfectly capable of producing the waves it needs, but somehow evolved to need the sound of crickets to help it along.