A few things I have noticed. The issue only occurs on posts where I have uploaded the image using the media upload for that post and that is the only post with the image. Or also it will occur if I upload and image to the image library, it will occur on the post where I use the image the first time. If I insert that image into a second post the issue will not occur.
If I create a new image post, and insert in that post an image which has been uploaded elsewhere, the issue does not occur. Therefore the two posts are essentially identical. The only difference is that in one I uploaded the image to that post and the image is therefore "linked" to that post somehow, it occurs on the post it is linked to. but does not occur on the second post which is identical otherwise.
For example: The first place I use this image HERE the issue occurs. The second time I use that image HERE. The issue does not occur. The two posts are identical otherwise.
The issue does not occur on posts which only contain a gallery.