Hugh McLeod is fond of saying....
"there is no limit to the market for hope"
When people contract a consultant, they're buying into the hope that s/he will help them to solve their problem. I agree with you that as long as you meet that need, you deserve your rate -- even if all you did was to help them find their own solution.
And you're also correct to say that confidence plays a big part. Just having a "we can do it" attitude and a willingness to look for solutions goes a long way.