This does not seem to be correct. I asked Kagi "does kagi build its own index". From the first result (on help.kagi.com):

> Kagi Search includes anonymized requests to traditional search indexes including Brave, as well our own non-commercial index (Teclis), news index (TinyGem), and an AI for instant answers. Teclis and TinyGem are a result of our crawl through millions of domains, focusing primarily on non-commercial, high-quality content.

[Edit] I guess it is possible that Google or Bing are hiding under "traditional search indexes including Brave".