As others have pointed out, I too have obtained much better results when using the secure email feature than when calling on the phone. I always get the impression that the phone CSRs simply have no power to do anything except the very basic stuff. When confronted with problems, they tend to read off the script and say that's all they can do. Email agents respond often times within 24 hours and, at least in my case, have always satisfactorily fixed the issues.
Does AMEX have two sets of CSRs? Is this a way of discouraging the use of their 800 number? I just don't understand the disparity in attitude and aptitude.