Yeah the "gravitational hum" would not seem to be the same as gravity itself having some inherent randomness. On the flipside, in a very real sense if the cosmological history of our universe is such that we exist in a universe with an always present indeterministic hum, then for our intents and purposes this is the same as gravity itself being random... unless we can devise experiments to study gravity in other universes with different cosmological initial conditions.
