That's an incorrect way to view it actually. 4'33" copyrightable essence is actually represented by the active production of its scoring. I.e. nothing. The background sound is not what makes it copyrightable. You can go ahead and sit at a piano for the length of the composition all you want, wherever you want, and you'll still be publically performing 4'33".
The rather humorous outcome, if one asks me, is that anyone who writes in 4 beats of silemce into a score should be violating copyright if we're going to be consistent.