MustafaD No they use Google and Bing indices.
@MustafaD, I suspect you are correct. Upon reading the blog again, I believe Kagi is attempting to distinguish between direct and indirect access to the Google and Bing search indices: "Because direct licensing isn't available to us on compatible terms, we - like many others - use third-party API providers for SERP-style results" (e.g., HasData or SerpAPI).
@Luis, can you kindly confirm and clarify whether and how Kagi Search utilizes the Google and Bing search indices?
P.S.: Interestingly, if you ask the Kagi Research Assistant (Experimental) "Does Kagi use the Google search index?", the answer is: "No, Kagi does not use Google's search index."