I think cloud companies essentially want the 4th amendment benefits of treating the cloud like real world private areas (e.g. bank lock boxes), without any of the obligations that come along with that.
The "reasonable expectation of privacy" in things like safe deposit boxes or storage units is based on the actual fact that service providers generally do not and cannot access the contents of those rented spaces. To apply that same reasoning to data stored in the cloud, we have to indulge in the fiction that various bots and sysops cannot in fact access that data, and do not routinely do so.
That said, I think the cloud folks are ultimately going to win, on the basis of Riley v. California (which is noted in Brad Smith's op-ed). I think Riley is technologically ignorant in glossing over technical distinctions between local and cloud storage that are relevant to privacy, but it all but says the cloud is protected under the 4th amendment. I don't know what's left to fight over.