I don't know if clinically I have or don't have social anxiety.
From my personal experience I do have a lot, not so much as you have, I think...but in my opinion by outgoing while fearing people at the same time is different than going around meeting new people, and hanging out with them.

As everything else there's a spetrum. I don't know who are those people you know who claim there selves to have social anxiety, but still do that... I don't do that.

I can answear in classes, and I kinda like it, I can have circunstancial talks with strangers. On the record I rather have a small conversation with a stranger that I will never see anymore, than talking with someone I know but don't feel confortable with. So being in a crowdy place with strangers it's not a feel bad situation.

But there's a thing about me. I like to talk and laugh. I love to joke around, I like to be nice to people. And even I don't give the true friend name to anyone I know, because I feary intimacy badly, I suspect if I wasn't so shy, if I didn't have the other problems I have. I would like to go around hanging with people.

Having social anxiety is not the same as being an introvert. But bad anxiety can mimic that. Can be thought as the same.
I would love to have the possibility to be outgoing in more than one or two contexts. But people are different.
In the past I use to though that I rather be alone than have company, but now, I doubt that to be true.