The advice not to rely on numbers is truthful, but is often casually spouted as if the numbers mean nothing. That is not true. If a fancy cut diamond has parameters outside of the AGA 1 and 2 numbers, most cutters would agree that there is some "fault" that might be better if it was not present. The problem is that diamond rough and economics combine to make cutters choose how to shape a stone other than perfectly nearly all the time. That is why it is such a skilled job and not done on a production line. There is an acquired art to it.
A diamond with a Cut class 1 or Cut class 2 grade is likely to be a good looking diamonds, but it depends on the skill of the cutter and the rough stone that was present before the cutter began. Some rough has inherent limitations so don't just say it is the cutter's fault if a stone looks a bit less nice than another one.
Read the rules of use of the AGA Cut class grades, too. You will see some degree of flexibility built in which makes the system workable and useful. There are many who will advise you not to rely on numbers. I support them up to the point where you'd make a poor decision by not looking at a stone before you buy it. However, cutters have found the AGA Cut class parameters of great use in perfecting their art. These charts were not created in a vacuum or meant to push sales of faulty goods on people. they were created to be helpful, honest and useful. I think many people have gotten better diamonds because of this information and few have been hurt. No one that I know of has ever complained of any problem created by this added knowledge.