I don't know why anyone would dismiss measurements so quickly. Like Craig said earlier, measurements are essential in fine tuning your system and, my personal experience with measurements and EQ lead me to believe they are essential in improving what you have. Like Craig's example earlier, I had a large bass bump in my room and the midrange bass was overpowering other notes. Without measurements and EQ, I could not have tamed that bump and the before and after difference using measurements and EQ was dramatic to me. EQ is not enough. You need to measure response in your room and even moving speakers 6-12" in your room can result in differences in response.
As for Axiom, I would simply tell people to do their research. Some of their speaker designs are less conventional and, as Bill has clearly explained, go against what a skilled audio engineer would design since those unconventional designs result in issues. The good news is that Axiom offers lots of designs and choice, so if you are deadset on buying Axiom they do offer speakers that have a more ideal design.