In this theoretical system, ideally it’s illegal for anyone other than the person who’s supposed to have the private key to have it - excepting some subset of legal reasons (e.g. parents for their children). So, the only business that would be asking for people’s private keys are the kind that are already operating outside of the law.
A PiHole functions has a full DNS server. You can configure it to serve any arbitrary records you like - which is basically how it overrides ad domains to prevent them from loading.
So, if you know the IP address that a particular domain is supposed to route to, you configure the PiHole to respond with that IP address for that domain. So, it doesn’t matter that the major DNS servers return junk because your PiHole never asks them.