The media library is certainly a little confusing, it isn't obvious from the user interface exactly how it interacts with blog posts. Perhaps at the very least it needs a few notes adding on the "edit media" page.
From experimentation it seems that updating the title, alt and caption fields of a media library entry do not update the blog posts containing that image. The updated values are only used when the image is newly inserted in a post.
If you delete an image library entry then it deletes the central copy which affects all posts containing that image. I would have expected that updating any field of the image library entry similarly updates all posts using it (surely that's the point of having the library rather than having to doing all image editing via the posts). Not very consistent - the image is a common copy, the attributes are not.
Allowing different attributes for the same image in different posts is of course more flexible. But it would be very cool if the "edit media" page had an option to apply the edit to all posts containing the image.