Robert,
Checking and unchecking the checkbox of the Group Layer (presumably added as an ArcGIS Layer File or Layer Package) will control the visibility of all layers within that group. The individual layer checkboxes will not change status - this is designed to indicate exactly which Layers will be affected when the user changes the visibility at the group level.
If this is a layer which will be frequently used in your Explorer sessions - and particularly if you are intending to deploy it to a user base via an Application Configuration - you could also consider writing an Extension Add-In which would search the map contents for this layer by name then set the visibility as appropriate. This would obviate users turning the visibility of all layers on then saving the map and closing - only for them all to be redrawn when the map loads next time.
Regards
Mike
