I guess there are two and a half possible mistakes here, which I'll address separately.
1. The Network is a toy. No. At least as far back as the Treaty of Bern (in 1874) the importance of the global Network is so obvious that national governments give up a little sovereignty to have it work better. Communication makes the difference almost everywhere almost all the time. Bern of course is about written letters, but the Telephone follows the exact same course, and so if you accept the Internet as a natural successor all the same things apply.
2. Maybe the Internet is not the Network? This argument looks completely reasonable in 1986 when IP networks are mostly an American phenomenon and there is a lot of X.25 out in the rest of the world. Maybe the Network will be X.25. By 1996 that's a distant memory, everything is IP. It's a done deal, the Internet is the Network.
2.5. Mistaking the Web for the Internet. The Web initially looks like a toy. HTTP/0.9 era Web has lots of toy-like qualities. Academics have been designing powerful hypermedia technology for many years by 1990, surely this half-arsed tech demo from a CERN guy who isn't even a Computer Scientist is a flash in the pan? You can make a better argument that the Web is still a toy in 1996 than the Internet, I don't think it's a good argument but it can be made -- however the Web is just an application. A competitor hypermedia solution that crushes Tim's Web but uses IP is still the Internet.