To clear this up a bit, "not being in any chat channels at all" means clicking on the "Leave" button in the Chat gump.
At that point, you are not in any of the listed channels at all. If you try to chat, you will get the message, "You must be in a channel to do this. Join a channel using the Chat menu on the menu bar."
And this will save properly once Publish 63 is available on your home shard. You will no longer auto-join the "General-Trammel" channel every time you log in.