This is completely wrong. Examine your GMail cookies if you don't believe me. The ones that grant access to your account are named "S" and "GX". You can prove

This is completely wrong. Examine your GMail cookies if you don't believe me. The ones that grant access to your account are named "S" and "GX". You can prove this by a process of elimination. Delete a cookie and see if you get logged out. They're set on "mail.google.com", not "google.com", so they don't get sent when you search. Furthermore, they're marked "secure" so they only get sent over HTTPS.