It might be a good idea to first define what the internet is. Tim Berners-Lee of CERN is given credit for inventing the web when he realized that html made web pages possible, eliminating the need for a more or less ftp based web. The first true multi-user time sharing system was Multics, which was started all the way back in 1965. The internet more or less runs on UNIX, which wasn't written until the Multics project was up and running.

In other words, unless the fictional model looks a lot like a LAN and includes relatively static web pages and allows general browsing and comes from before 1965, I don't think it qualifies.