Personally, I feel it comes down to your purpose for playing.
I feel that many musicians who wish to become proficient in every genre, do so, so that they aren't limited in the work that they can get. Or because it's the a 'law' in some, as of yet, unwritten book of guidelines for musicians. Because someone can play more styles, that makes them a better drummer/musician? I think that's putting what it means to be a musician, in a box. What if someone wanted to created their own style - and were totally uninterested in the style's that already exist? Does that not make him a great musician/drummer, if he becomes very proficient in such? It would seem that being labeled a great musician/drummer .. ultimately comes down to one's ability to be sought offer by artist's, in a myriad of genre's.
While I commend the effort and dedication it take's to achieve such - it shouldn't be the end all and be all for a musician. Some people, like myself, are more concerned with discovering new musical ideas. Why be limited to learning music of various genre's if your ambition isn't to be a 'working musician'?
Music is, inherently, limitless, I feel. Their is no end to what one can do with music .. however, if we restrict ourselves to what has already been done, then we quite possibly deprive the world AND musicians alike, of something entirely new & exciting
Just because 100 great musicians said it, doesn't make it a law. NO ONE owns this. If you want to work in the INDUSTRY, then you have to conform. That's just the way it is. If you're more concerned with finding your OWN musical voice, then you explore the depths of the infinite musical universe ... and leave a legacy of originality, for all those you left behind, to aspire to.
Music is whatever you want it to be. Don't let anyone tell you otherwise. No matter how passionately, or eloquently they may state it. No one will ever be a complete musician, 'cause I doubt our human minds can truly fathom what that means. You can be complete in being able to play what has exist's to play ... but that has it's own limitations, as does the musician who can't play any of them, but seeks to play their 'own song'.