HTML currently says UAs should allow the following:

"""
Select and move non-editable elements nested inside editing hosts
UAs should offer a way for the user to move images and other non-editable parts around the content within an editing host. This may be done using the drag and drop mechanism. User agents must not, in response to a request to move non-editable elements nested inside editing hosts, generate a DOM that is less conformant than the DOM prior to the request.
"""

The same should probably be said about images, etc.