When in doubt, double down. Is that your approach?
Firstly, you apparently didn't read my comment that I wasn't discussing how apt works, only yum.
Secondly, the critical issue that you are missing is that if I install a package from an alternate repository (eg EPEL), my systems don't tell the main CENTOS mirrors about those EPEL packages. This is really the key difference between yum and what Microsoft is doing: Microsoft knows about everything installed on a system, irrespective of origin.
Thirdly, the mirrors only learn about installed packages if they are updated. If I install from a DVD and the package is never updated, no mirror will ever know that I installed it. I can install non-default packages from DVD should I so choose.
Finally, there is no fingerprinting involved in the yum transactions. If I have multiple machines behind a single IP address, the server doesn't have sufficient information to distinguish them. As well has having insufficient information to fingerprint individual systems, no user information is transmitted.
In summary, yes I am leaking some information, but it is benign.