I’m aware of what the central limit theorem is, but I’m confused as to what you mean here. Do you mind clarifying? It sounds like you’re saying the CLT leads to deanonymization. I don’t see how the two are related.
Take several measurements and average them. The variance scales like 1/n_samples, which can take you from city-block resolution to building resolution quite rapidly.
There are conditions for the central limit theorem to hold though. One can generate random noise which violates them. It's certainly hard to guarantee privacy, but it's not trivially easy to hack if they're halfway smart about it.