I don't know how Sony Pictures internal systems communicate, but I'm pretty sure they don't need to have direct access to world+dog in order to do so.
What seems to have happened here is that by network-based manipulation of external firewalls, direct communication routes were established between malilcious hosts on the Internet and internal systems. You can avoid that and still maintain e-mail communication by relaying your mail over something other than TCP/IP between your internal-facing and external-facing systems, for example.
And there are actuallly very good productivity reasons for restricting Internet browsing to dedicated computers on physically separate networks - it considerably reduces the amount of the day your staff spend on facebook and amazon.
I'm amazed the "Internet of Everything" mentality still prevails. It was a utopian dream of the 1980s and 1990s but we now have very clear evidence of what happens in practice with universal connectivity - a dystopian nightmare in which governments and criminals are in competition to gain the most effective control over people and commerce.
Perhaps we can ask Sony Pictures how their present productivity is looking compared to, say, RKO?