Create the page, "MyPage"
Add an attachment MyImage.jpg to the same page
Edit the page adding the image link manually or with the wizard
The page shows OK with the image.
Rename the attached image through the Eidt menu (2.X) or Properties (3.X)
Rename the file from MyImage.jpg to MyImage2.jpg and save.
Return to MyPage to view it and you get an error
Unable to render embedded object: File (MyImage.jpg) not found.

Alternatively in 2.X, you have the extra menu:
Update Links? Links to this attachment from other pages will no longer work on rename/move. To prevent this, these links need to be updated. Update links?
Setting it to YES (default is NO) make no difference even if you give it some seconds after the save in case in would be a background process doing the update.

The proper behavior should be of course to look for the references to this image in all the pages and to update the pages.

NOTE: If instead of an image insertion, you do a link insertion then everything is fine, the page is properly updated so the fix should not be too complex to implement.

If the page content needs to be updated, the last modified DATE and NAME should not be updated to the current user.
This is not the current user doing the change, this is the system on behalf of the current user.
Not sure how you want to address this but if you don't you could have a user modifying pages he has not access too.
And if a watch is involved, I guess that it is better if no email should be generated for this.
Just my opinion.