I think Google, and likely Anthropic, indeed do honor the settings chosen by the user. For Google in particular it'd be very surprising if they didn't. That's also why both do everything they can to trick users into allowing it.

OpenAI, I wouldn't be surprised if you were right.

unfortunately the history of these big tech companies has shown that they do not care about data privacy and are even willing to lie about it. but I guess its irrelevant, in practice you have to assume the worst anyway since there is no way to verify it

The models doesn’t get better by themselves. You’re naive.