I heard years ago that DARPA bought the data packet switching idea from someone, I think a university professor.
The thing about DARPA is there are no “DARPA labs” where things are designed, built, or coded. They essentially develop requirements and fund industry/FFRDCs/college labs to develop things.
Heck, the guy doesn’t even understand the protocols he’s talking about. He’s describing Ethernet as a protocol for connecting networks together. This is false. Ethernet is a local area network protocol for creating a network. He does mention TCP/IP, and that’s the important one for connecting networks together. Ethernet just happens to be the protocol which won, but there have been plenty of various LAN protocols over time.
I can remember using ARPANET back in my undergrad days before the internet really got opened to general use. Back then it was restricted mostly to universities, defense and research labs.
It was when Tim Bethers-Lee came up with the html protocol at CERN that the internet exploded. Before that it was limited to email and netnews groups which were just text based forums. I spent a lot of time on those old forums.
I can still remember when the post doc came into the lab to show off Mosaic to demonstrate this new web thing. The software was extremely buggy and there was about nothing to connect to in any case. Amazing how far it has all come.
There is some truth to the contention that the government invented the internet, but only in terms of the DARPA projects as you say, though the guy invented html on CERN’s dime which is government as well. Fully blossoming it into what it is today was a matter of private enterprise and it really does show the value of the free market because the whole internet/web area of commerce was so poorly understood by governments that they didn’t vaguely know how to start regulating it. Thus it was not strangled in infancy.
In it's zeal to push the use of UNIX as a major mainframe OS, AT&T gave thousands of it's 3B mainframes to colleges across the country - and it was to these colleges, and AT&T facilities, and military bases that AT&T hooked together that became the first 'network' between computers.
When the government became involved and DARPANET used this network, and the first network communications became a reality. Simple text communication via 'email' became a part of that communication later. But prior to email sharing of major documents was the first BIG THING on that network.