Thanks for your feedback all ... I have managed to fix this. What I suspect was the issue was the following.
When looking at properties for the facebook.dll file in Windows Explorer (Windows 7), there is a new property under the "General" tab which says:
"This file came from another computer and might be blocked to help protect this computer."
Then there is a button with an "Unblock" title.
After clicking the "Unblock" button, this property disappears. I am not sure what unblocking this this actually does, but at least my ConnectSession(...) works perfectly now.
Just to be clear, I also played around a bit with other security issues (i.e. adding FullControl permissions for Everyone), but I have rolled back all those changes and cleaned the solution and restarted IIS, and the SessionConnect(..) still works.