The captive networks I have seen do the opposite. HTTPS does not go through until an HTTP link is accessed to generate the 'I agree' page. Probably why neverssl.com exists in the first place.
What makes you think it isn't privately owned? It's true that the domain can't be bought, but you still hit a Verizon server when you go there.
And if you're using an iDevice, you might as well go to http://captive.apple.com, which was designed for the purpose of authenticating to hotspots and Apple already knows who you are anyway. :)