Gary: they only need to access one program. What happens if one of your users rightclicks one of the shortcuts? Does the usual rightclick menu open? Does the menu have the Properties option?
My users don't get the shortcuts as they don't reach a desktop. They open the RDP shortcut and the program opens automatically. When they close the program, their terminal session logs out. There are a few ways to accomplish this. One is by group policy and two is by editing the RDP shortcut with a text editor, the easiest way is by opening up an rdp shortcut on your 2012 server by going to run and typing mstsc. When you click options, it will maximize the window an show the tabs. Look at the program tab in particular. Add your program there and then save the terminal server shortcut. Place that shortcut on their machines and they won't have full desktop access any longer.