They need Add/Modify/Delete permissions on the files or they won't be able to share the BE.
When the first user opens the application, Access has to create a lock file for the BE. That means that the user needs to be able to create files in the folder that holds the BE. When the last person closes the application, Access has to delete the Lock file. That means that the user needs to be able to delete files in that folder. When the user makes any data changes, Access makes notes in the lock file to keep track of what is going on and so the user needs Change permissions.
If Access cannot create the lock file on the BE, It opens the database in exclusive mode and that prevents any other user from doing anything except read the data. If the last user does not have permission to delete the lock file, it remains abandoned. This will eventually cause a problem if no one can delete the lock file because it bloats.