Earlier quoted context omitted.
This isn't about averaging over all your submissions, it's about averaging over the entire population (in this case, of iphone users, ~1,000,000,000). Data about the entire population, e.g. how many people click this button, or how many results do most people get from this page, or what kind of things do people take pictures of, i think are safe.
If you average over the entire population, it's privacy preserving indeed. But this averaging happens on the side of the server, not the client, so I can't really verify whether the server stores away the deltas of interesting/all users or it averages really all user deltas. I know apple has some means to anonymize users by using random changing IDs instead of the apple ID, but they can correlate it to an apple ID vi…
For your example, sure it's possible for the server to do something you don't know. But it's the same people on the server doing the aggregation as on the client doing the obfuscation. If they really wanted they could easily e.g. set the seed for the noise to be based on a key which they have on the server, which would be very difficult to detect. I think you just have to trust that apple wouldn't let that happen.