Actually, the initial development was done almost entirely by think tanks (Rand Corp., BBN, etc.) and academics, with the crucial piece being supplied by the concept of packet switching, invented by Paul Baran at Rand Corp.
The essence of government is centralization of power over individuals. The essence of the internet is decentralization of communication among individuals.
The internet was a revolutionary invention because it solved a revolutionary problem: how to maintain communications after a massive nuclear attack. Pentagon (DARPA) money was behind most of this because it was the Pentagon that was responsible for solving the problem. More to the point, the key technologies that the internet depended on were the transistor (AT&T/Bell Labs) and the integrated circuit/microprocessor (Intel).