Actually it's not. The Internet that we know today is really NSFNet that was created because the DoD was sick of freeloaders riding on ARPANET. The DoD had very little input on the creation of NSFNet. What was ARPANET is now NIPRNet.
This is one of the many things that I learned by reading Where Wizards Stay Up Late: The Origins Of The Internet. It's a fascinating look at how the Internet was created and focuses mainly on the financial and management side of the creation from about 1965-85.
One of these things is not required for my browser to work. Hint: it starts with "govern"