Hi Harprit,
Good to hear it's working, and thanks for the clear write-up. That's not a setting you're missing, it's a real inconsistency on our side, and your diagnosis was right.
There are two ways an image can get into a post from chat. One goes through our image tooling, which downloads the file into your media library and serves it from your domain. The other is the assistant simply writing the image tag into the post body with the source URL still on it. WordPress accepts that markup as-is, so nothing pulled those files local. That second route is what your CEBU guide hit.
Auto-generated posts don't go through that path, which is why they behaved the way you expected.
Fixed in 2.0.68. Images added through chat are now downloaded into your media library first, whichever route they came in on. It'll reach you through the normal plugin update.
Your preference is the right one, for what it's worth. Files in your own library survive the source going away, and WordPress can generate properly sized versions from them.
For the CEBU guide, re-uploading those few by hand is still the quickest fix. The update won't retroactively rewrite posts that already exist.
Thanks for flagging it. This one was worth fixing.
Christian