I also struggle with the statement about SA not being noticeable to others..
I can probably believe that in my day to day interactions it isn't noticeable, and maybe that's what I should work on telling myself.
However, when I have an extreme bout of SA, I know it is noticeable because people have commented and laughed at me in the past.
An example is when there was a big meeting that the whole company I worked for attended and we were all shuffling into the big drawing room of a hotel. I was feeling overwhelmed, the usual dry mouth, red faced and sweating. Goodness knows what my mouth was doing!.
A supposed friend of mine was standing across the room and looked at me, he turned to the person next to him, sniggered and said "look at Oli!", and he wasn't even subtle about it. Which made me feel great as you can imagine.
Pretty much the same thing happened when I was at a group meal in a restaurant too, something I have always found hard( I think its to do with being trapped in a seat whilst surrounded by people).
Anyway, I definitely feel that this course is helping me slowly but surely.
A big difference I have noticed already is that even after an anxious experience I have managed to not beat myself up over it and let it go. In turn this has reduced my overall anxiety.