You need to be able to cite a source, ideally a case or specific law, on such a claim because no one else I know holds to that definition. A link to a Wikipedia article about a different concept does not satisfy, because it does not cite a legal definition of free speech by US courts.
You've levied a pretty heavy claim with nothing but your word as evidence for it.
I remember thinking "oh yeah, that makes sense, they wouldn't view free speech in isolation but as a tool of the democratic process."
No. That's never been the case. Your room is open to all and people who want to listen aren't prevented from going into it.
However, I'm also not obligated to host you in a room I own. The government guarantees my freedom of association as well. You want to opine, do it in your own room, or do it in places owned by the public at large.
Your recollection of what you were supposedly thinking doesn't mean you didn't misread what was written either. If you want me to even consider your claim, you are going to need a source on it. Because, like I said, it's a heavy one.
The owner of an auditorium or hall is allowed to not give platform to anyone. They get to decide who gets heard.