I think that's an incorrect oversimplification. The Internet didn't grow from ARPANET like a seed grows into a tree. ARPANET didn't become bigger and bigger until it became the Internet. The Internet was the merger of many networks and many of them never communicated with any computer in ARPANET and we're developed with absolutely zero funding from the United States government.
I guess it’s a matter of interpretation. Of course every computer connected to the internet is not government-funded. But in this context we’re talking about the origin of the technology and protocols that allowed the network to exist at all. By the time the internet got bigger than ARPANet, CSNET, and NSFNET (all government funded), the protocols were pretty much settled, and that’s what everyone else’s network used to become part of the internet. If the government hadn’t gotten it to that point, there would be no internet.
