Upload an attachment to a page, and log in as a user without permission to create attachments in the space.

The user can view the attachments page, and select 'Properties' from the dialog. This makes it look as though they are able to edit the properties. When they try to save, an error is given:

 You do not have permission to move this attachment to the space SPACENAME. 

This error is confusing - it doesn't explain to the user what the real problem is.