Actually, that's not true, and hasn't been since 1985.
The backbone (as you so quaintly put it) is composed of high speed circuits owned and operated by huge telle-com companies, little telephone companies, and private parties.
Some parts are owned by other governments, the British, Canadian, etc manage the tell-co in their respective countries.
Yes, you are correct. The bulk of the data traffic is carried over telco networks, and the root domain servers are "owned" by a quasi-public consortium.
However, if you don't think that the Feds can sniff any packet they like and at nearly any point on that quaint "backbone", you are sadly mistaken.
Network security, until very recently, has been by bread and butter for years. I'm here to tell you that Prime Choice is right on target: if you want privacy on the "public" network, it had best be heavily encrypted. Even then, if they want to break your traffic badly enough, they will eventually do just that.