You can make an analogous argument about the traditional corporate site to site VPN, which is a point to point link between routers that bridges two non-virtual networks. By your standard, calling that a virtual network is only true in the degenerate sense.
I see your point about the possible meaning of "private", but I don't think that quibbling over the semantics is useful for much besides gatekeeping. There were plenty of corporate VPN links piping Internet-reachable IP addresses, just as there were plenty of VPN links with broken or nonexistent crypto.
Disagree. "The network", in the sense that my PC, and Bob's PC in the next town, and the server in our colo space, are all on "the network", is virtual, in a pretty essential sense. Even if 68 of the links in the network are physical wires and only 2 of them are virtual, their existence changes the character of the whole. In the same way that we have an "international network", that would be important to think of and treat as international, even though it only has one cross-border cable.
The common-sense meaning of "private network" was, and is, a network that is private. I had one with a bunch of my university friends - we ran our own network services that we wouldn't trust to the wider world, like we had back when we lived together and really did have our own private network.
A point-to-point line to the provider's router that then bridges you onto the public internet is a "private network" only in the most degenerate sense.