Your requests are still forwarded to a third party with a Pi-hole. They are sometimes cached and sites you have blocked do not resolve, but choosing a DNS provider is still required.
Only non-cached requests go to a third party. And I don’t think there’s an easy way to prevent this unless you get a hold of all the zone files and copy in bulk.
What’s nice about pi-hole is that you get one request to sites like google.com until the record expires in the cache. If you use 8.8.8.8 as your dns you might end up requesting the same domain name a bunch of times depending on how your client caches and the caching is at 8.8.8.8. So dns will see lots of requests to the same domain.
In a network of just a few computers, are there really that many cached requests? Local DNS caches will already cache short term and TTL of most domains is probably too short to get much caching beyond that.
Looking at my dnsmasq statistics, only 16.3% of 10,776 queries in the last 24 hours have been answered by the cache. Another 21.7% never left the device, since they were in the block lists, but that still leaves 62.0% of queries to be returned by 1.1.1.1 and 1.0.0.1, which is my external DNS provider.
Although this doesn’t count on-client caching, it still seems to back up your guess and my original comment.
What’s nice about pi-hole is that you get one request to sites like google.com until the record expires in the cache. If you use 8.8.8.8 as your dns you might end up requesting the same domain name a bunch of times depending on how your client caches and the caching is at 8.8.8.8. So dns will see lots of requests to the same domain.