They can claim what they want; the fact remains that I have to trust them. If I use Brave or DDG or even Google, I can do things to obfuscate my identity from them. Kagi is the only search engine that requires users to authenticate, and ties that authentication to a method of payment that can be trivially tied to the user's identity. As far as the user is able to verify, that makes them the least private search engine.

Even if they're telling the truth, if they receive a national security warrant, they'll start collecting that information secretly. Hence my interest in a warrant canary.