You are right and you cannot set up a view which shows calls for organization. I do not know of any easy way round this but I think there has been an enhancement request for this for a long time but nothing changes.
If you log into the service pages with an application account instead of an SP account you do see the calls for the workgroup. Of course for an application account you have to buy a license. However you can change the jsp file to behave the same way for SP and application accounts. If you check the ListServicecalls.jsp file you will see that there is a check on "IsSpecialist" or something like that. This just checks if the account is an application account or SP account. However if you play around with that you can get the desired result.
What I described above can be used to let a SP see the calls for the workgroup but not for the organisation, which is what you ask. However that is also possible but requires recoding the jsp. Using the Web API you can make a jsp file that uses a custom view to show. In attachment a jsp file I wrote to list incidents using a view called Plasma. You can do something similar for servicecalls. Hope this helps.