I don't understand their assertion; Kagi has an incentive to collect data... Most companies do. The incentive is money. Kagi would not be the first company to collect data to monetize it later. And Kagi dreams big about all that data:

Instead of being scared to share information with [your search engine], you will chose what data you want it to have and volunteer your data only after knowing its incentives align with yours... The search will be personal and contextual and excitingly so!

https://blog.kagi.com/age-pagerank-over