How do I get Mountain Lion Calendar to subscribe to iCloud calendar another user invited me to?
The issue is that the calendar needs to be made public.  This does not mean that anybody can see your calendar, just that anybody can subscribe to it if they have the URL you send to them inviting them to subscribe.  Calendar does not appear to have the ability to subscribe to a non-public calendar, since you don't have to enter your Apple ID to use it, and iCloud uses this to authenticate that you are authorized to view a private calendar.