In the US you are a "free" citizen in an "open" country. You are free to go anywhere you want on open roads. This doesn't give you the right to trespass and go into anyone's private property. If they have a fence up, you have to stay out. If they're having a yard sale, you can come in.
If Alice wants to let Bob on her property and not Eve, that doesn't make the US any less of a "free and open" country.
This is what is meant by "free and open" web. You can attempt to reach any endpoint you want without restriction, but the endpoint itself has private control over whether you are allowed to its contents or not.
Anything less is not actually freedom, because then the endpoints' freedom to determine who can use its private property is being denied.
A web that is not "free and open" is one in which your attempts to reach endpoints are interrupted and allowed or denied by a third, censoring entity. (Usually the government.) It has nothing to do with how those endpoints would respond to you on their own.
It's a nuanced (and sometimes nebulous) concept, and I don't really understand what the GP post was getting at, but here's a better attempt than mine to get a handle on it by Tantek Çelik: http://tantek.com/2010/281/b1/what-is-the-open-web