The real problem is that "direct access to servers" is not a specific term. Given the various definitions it could have, everyone could be being truthful.

Some would interpret "direct access" to mean root level access to their entire infrastructure, which sounds absurd to me, yet some people seem to believe that's what's happening. And it's my understanding that this is what Google, facebook, etc. have been denying. They could instead be giving "direct access" to an FTP server or some other portal set up to provide the requested data, meaning that Snowden and these slides are being truthful in that context.

I also think it could be argued that we all gain "direct access" to Google's servers every time we type "www.google.com" into a browser's address bar. It is just not a useful term, and should be replaced with something more specific in all these instances.