If the point is to improve public trust “don’t worry, we manipulated the data to make it more anonymous, but we pinky swear that we didn’t manipulate it in a way that changes the results” is not a good approach.
Nobody's saying "tamper with the evidence to demonstrate favourable outcomes" here.
And if tampering with the data to favour the data donor were a concern in the first place, then it should be a concern regardless of whether the data donor said they followed further anonymization protocols or not.
Yeah, so you have badly misread my point, and you're arguing against something completely unrelated to what I'm saying.
Of course you can add randomness to the results to hide individuals without messing with the results in aggregate. That's obvious, and I'm not disputing it. The issue is that that's a PR nightmare. Nobody here might be saying "tamper with it to change the outcome", but I guarantee you that people out wider media will accuse the CDC and Pfizer of doing exactly that. I can see the chyron now, "CDC ADMITS TO MANIPULATING DATA".
Organizations like the CDC need to think not just about how their message will be heard, but how it might be twisted and abused by bad faith actors. You are absolutely right about how you can safely introduce randomness, but you are completely wrong about how that will be handled by the public after bad faith actors get their hands on that fact.
But I don't necessarily think this would go down much worse than "Big Pharma refuses to share data, what could they be hiding from us" bad faith actors.
At least in the 'inject randomness' scenario you can do some damage control in the media by bringing in experts to explain how this is a valid thing to do and how it protects the average joe from having their lives turned upside down just because they foolishly agreed (or worse, did not agree) to have their data collected.