The "View on site" feature should work even on a component stored in a parent publication (which is usually the case). At the moment the "View On Site" feature only works on Local components, not shared/inherited components.
Currently View on Site provides functionality in context of current publication. It works with any item states: local, local copy or shared
Are you expecting that View on Site for current publication should provide you info for selected item in context of entire BluePrint structure?
The "View on site" feature should work even on a component stored in a parent publication (which is usually the case). At the moment the "View On Site" feature only works on Local components, not shared/inherited components.