Shal,
Thanks for your interest in my issue.
What was happening is this:
When I am the OP on a message, Gmail doesn't show it in my message thread until someone replies to it.
When I reply, via Gmail, to a message in an established thread, Gmail shows my reply message (also in the Sent folder) as part of the thread. When I had the "Send me a copy of my posts" option clicked, I would see my Sent message as part of the thread AND immediately following that, I would see the GIO message sent out as my copy of the post.
My experience is that Gmail doesn't show my emails in my inbox UNLESS they're part of an ongoing thread that Gmail can link together via replies and Subject lines. Once there is a sent and replied thread going, everything in the thread has the same label (or is in the same folder, but it's Gmail so they use labels).
Does that makes sense?
