Right — there’s not a lot of unique bits for the number of people in the world[1], so fingerprinting like this can be really powerful. It’s possible, however, to keep these bits of information apart, so they can’t be correlated (including, as I saw earlier in one of these posts, not submitting them at the same time).
It’s also true (as @dalto says) that the design of the internet means any receiver gets an IP address, which is possibly identifying information and a likely key that could be used for correlation. I personally would be fine with a mechanism where the initial receiving system doesn’t forward any IP address information to the next step, severing everything. However depending on the sensitivity of the particular data[2], that might not be reassuring enough. We could, however, use Tor, or I2P — or even some sort of peer-to-peer onion-routing scheme devised specifically for this.