I tested it for about 10 mins with Blade Rush, Blade Storm, Crippling Throw, the damage is the same.
What you might be experiencing is min-max damage. I crit between 3 - 3.5k with Blade Storm without Precision Slash and the Proc does not change a thing.
are you using precision slash off of the gcd? i find that my ps uses up my oppertune strike. i br and then slip it in during the gcd so that master strike and bladestorm get the effects of ps.