I work at Kagi. This is a very reasonable fear to have. We do actually not store the data, but of course you'd need to take me at my word for this.
That said, if we did lie or change that, we'd be in immediate breach of our privacy policy (https://kagi.com/privacy), and as a result be a very easy target for a lawsuit. Given that we're intentionally not VC backed, between the horrible press this would be and the actual costs of fighting such a lawsuit, I expect not much would be left of Kagi afterwards. We are liable to users, in a pretty existential way.
That said, if we did lie or change that, we'd be in immediate breach of our privacy policy (https://kagi.com/privacy), and as a result be a very easy target for a lawsuit. Given that we're intentionally not VC backed, between the horrible press this would be and the actual costs of fighting such a lawsuit, I expect not much would be left of Kagi afterwards. We are liable to users, in a pretty existential way.