I do see yours, but I think you are missing mine. They do not claim or desire to have any functional weapons skills. It is purely performance, they know it, we know it, and anyone that pays an ounce of attention will figure it out. Why should they have to learn "real" weapons work if that is not their interest, or something they claim to have / teach?
The title does reflect what they do, as the title is meant for people doing what they do. They are champions in the sport of doing a performance with a weapon, that is what they claim, and that is what they are.
It is an artform, one that requires a great deal of athleticism and dedication, It is a martial art, and it is a performance. It is not a combat sport, or a self-defence system. It has champions, in "Forms" and "Forms with weapons".
Where is the dispute?
I think it is here:
And my take is that they are, as far as their goals with the weapon go, they are trained in the correct use of the weapon. Maybe not "Correct" for other purposes, such as application against a live opponent, or traditiona forms, but that's not what they are training for, so those methods would be incorrect given what they want to achieve.