In the keybase Web client, all crypto happens on the browser. The server knows no keys or data in plaintext. Of course, you'd have to audit the front-end JS code to believe that claim.
But our intention is that the only way to compromise the Web-based tools would be to insert malicious JavaScript into the client's browser. A read-only compromise of the server yields only encrypted data, and the server never has access to the decryption keys.