I was having this same issue when trying to subscribe to an ICS file on a web server. After lots of messing around with things, I discovered that the server was not sending the correct content type in it's response headers.
I added the custom mime type "text/calendar" for files ending in ".ICS" to the server's configuration (luckily this is a server I have control off) and it works fine for me now.
It looks like Calendar requires the mime type / content type to be:
You can check the content-type your server is providing in it's headers at the following site: http://urivalet.com/. Just paste the URL of the ICS file you are trying to subscribe to and scroll through the headers to see the value for "Content-Type". Let the server administrator know if it needs to be changed to text/calendar for *.ics files.