There have been reports of Cloudflare and other DNS providers not returning an IP that was subsequently returned by another DNS provider. Examples I recall were a German bank and a British telecom domain.
It has nothing to do with the ownership of Cloudflare. Quad9, for example, is headquartered in Berkeley, CA.
I am located in US - ran dig on aljezeera.com to Cloudflare, Google, and Quad 9 and received the IP in each case.
I think that is where your solution lies. It is not a Pi-Hole issue.
That said, if you run unbound as your local DNS resolver, you will avoid any third party DNS filtering. It's an easy setup.