Yeah so they proxy the requests so the AI companies can't tell what you in particular searched for because the requests are mixed with other users, but ultimately there will be an AI company in the mix somewhere and the search query needs to be sent to them to work. The search results themselves are also used as the contents of those is what the AI is summarising.

I know we are talking about using AI, but Kagi also lets you turn this off if you don't want to use it (by default it only shows if you use a question mark, but you can also turn this off so it doesn't show even with a question mark).