That makes zero sense. Where did you get that idea from?

For reference, here are their docs describing key management. https://tailscale.com/blog/tailscale-key-management

The public keys are stored on the server (by necessity) but not the private keys. The actual connection is directly between two of your own machines, or routed through a DERP server (encrypted end-to-end) in rare cases.

But if you’re concerned, you can instead self host headscale or netbird.