DNG permission required to allow folder moves?

Interestingly, the minimum you need is "Create an artifact", not "Modify an artifact". Of course you can narrow it further down to a specific artifact type.

This answer is not correct for 7.0.  I have users who have the permission to "Create an Artifact," "Modify an Artifact," "Create a Folder," and "Modify a Folder" and yet they still can't move an artifact from one folder to another. 

Through trial and error I discovered that in version 7.0 moving an artifact is considered a deletion.  If you turn off the option to delete the artifact you will not be able to move the artifact to a different folder.