IMO the burden should be on Google to prove that they don't. The flow of personal data through their systems is opaque and they have plenty of incentives to monetize the data.
Sure you can. Apple does not run its image classification on your images using its cloud servers. You can test this by stepping inside a microwave or other cage and seeing that image classification and search still works on the iPhone.
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On the other hand, what Apple does with your photos that you allow to be exfiltrated through iCloud... that's your own stupid fault.
You definitely can [0], but this one would probably be hard for google without significantly modifying the architecture of gmail in ways that would remove its revenue model. For example, they could open source a client that had audit-able end-to-end encryption, but then they couldn't optimize ad revenue by aggregating and mining large email datasets.
> a proof demonstrating that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general