Wow, looks like they just updated that page and removed all references to their external indexes. Very shady stuff, Kagi. I'd go as far as to say they are now lying by omission.

The archived version of that page from March does open with (emphasis mine):

Our data includes anonymized API calls to traditional search indexes like Google, Mojeek and Yandex, specialized search engines like Marginalia, and sources of vertical information like Apple, Wikipedia, Open Meteo, and other APIs.

Then it goes on to say:

Kagi's indexes provide unique results that help you discover non-commercial websites and "small web" discussions surrounding a particular topic.

Now reading between the lines, and more importantly knowing how much sheer capital goes into indexing the entire web, I can say with much certainty that Kagi is probably powered mostly by Google since it and Bing (which they aren't using) are basically the only meaningful players in the space. Yandex is for the Russosphere, and Mojeek is nice but nowhere even close to Google or Bing's coverage. By their own admission Teclis is more narrowly focused and not meant to replace Google's index. So I'm going to go ahead and call them big fat liars.

I wouldn't even care that Google is their main index, that's fine and they can't be expected to compete with the billions of dollars Google spends on indexing. But the lack of transparency and shady business practices are a big turn-off for me.