Interesting stuff. A colleague of mine posted this ( he has since taken it down) and responded very negatively to it. I could see my compatriot's opinion but I also think Branford is making a point (perhaps with a very blunt instrument, but a point nonetheless).
I have and have had many great students. They worked hard, studied, and looked at their abilities realistically without getting their egos involved. I have however, run into some players who don't want to work or research and pretend they're a lot more accomplished than they actually are. My colleague also mentioned people he worked with and their poor interaction with Mr. Marsalis and that's when I felt I had to mention my own experience. I played with Michelle Gregoire's band when we opened for Branford's quartet in Winnipeg a few years ago. Not only was he kind and gracious, but he invited us all up to play with his band during the concert. Not only that, he insisted we join him after the show for the food and drink the promoters had provided for him. We had a very lovely evening chatting about (what else?) music. I get the feeling that if you show him that the music is important and you are working diligently and honestly at it, he has plenty of time for you. In the clip above, I took away that a lot of people try to study with him as a resume bullet, and are trying to get him to feed their ego. I doubt he has much time for that.
Let me make this perfectly clear, I would NEVER, EVER, make a comment like that regarding anyone that has studied with me. I also think though, that many points of view (just like many types of music) are valid, especially if they're coming from an honest place.
See ya soon,