I did the following on a 6.2 website:
Created a group "Content Editor" as a security group
Put an ID into the group
Added the content slider to a page
Provided Edit authority to the Content Editor group.
Configured the module
Added a few pictures as admin
Logged out then back in as the content editor user
Clicked on Add Slider in the manage menu
Clicked on File for the source of the picture
At this point the browse link is not available so the content editor is unable to add pictures.
Until this is resolved, I am the content editor for the slider so I would like to have this working.