The editing, the selection of that particular iteration as being the "right" one is part of the copyrighted material.
And it isn't merely generated by a pseudo-random process, it's generated by code written and adjusted to produce a sound within certain parameters, with variation within those parameters provided by pseudo-random perturbations.
That said, I'm sure you could also record the sound of birds chirping in the dawn chorus, with even less input from the recording individual other than selecting a particular portion of the recorded audio, and copyright that.