Can Anxiety Be Rationalized Away?

So, I've been reading sections of The Anxiety Book by Dr. Davidson, and it hasn't really offered me anything useful. Mostly, he's trying to help people who have recently realized they have an anxiety problem. He tells the reader to identify negative thoughts and work toward replacing them with positive thoughts. And also to look at anxiety-causing situations rationally. Try to find the core fear and rebuild your attitude toward it.

For example:
In the case of a man's stage fright, the core negative thought was,
"If I'm not perfect, they'll reject me as worthless."

The rational response was,
"I have no real basis in my experience for believing that if I say or do something imperfect, I will be judged so severely. I get nervous when I think people aren't listening - that's when I repeat myself or stumble over words and become convinced that people think I'm stupid or worthless. But I never harbor such bad thoughts about people who are nervous while speaking. . . .Most people are probably like me - dwelling on their anxieties, not focusing on my lapses. . . "

Mostly, what it comes down to is finding out what lies underneath the anxious response. WHY are you so afraid to write your name in front of someone? WHY can't I go to the gym by myself?

Okay, I'm still working on that one. I don't know if I've figured out the core negative thought, or if rationalizing actually works like this doctor says it does. What do you think? I tend to see progress with immmersion and positive experiences.