It's "possible" but I don't think you'd want to. So I guess the answer to your question is yes.
I'm not quite sure what exactly he's getting at, but it could be another case of telling a newbie to do something extreme in order to get him to do something a little bit. I've had several people in lessons exclaim "I AM!!" as they ride by me and I tell them to bend their knees. They think they are, but their legs are bone straight. Sometimes you have to tell these people to sit in a chair to get them to bend their knees at all.
As for what is the "right" amount to bend your knees, I would say in my opinion, you only want to use your knees for suspension purposes - not to "get low" unnecessarily. That is, you never want your butt to be hanging way off the board to the inside of the turn if it doesn't need to be. In other words, you don't want your butt leaning into the turn more than the board is tilted up.
For instance, if you look at this picture, my butt is quite low, but the board is angled up quite high. My butt is still "over" the topsheet of the board.
Of course, I ride at 63 degrees and I don't race, so this is all based on that. At 45 degrees, technique would be different. It would probably result in a little more "chair sitting".