When a company performs a number, especially when the number is new, directors have a desire to restrict video recording because they are trying to protect their creations. Believe it or not, this has happened. I guess its pretty much like grabbing the words from one song and shamelessly putting them into another. I have even heard stories where people have gone out of town and have witnessed groups performing numbers created by other dance companies. The material apparently was shamelessly copied from a video recording.
People usually say that imitation is the best form of compliment.
But its only natural for a creative artist or performer to get offended when someone takes from them without their permission. Not all instructors are against being taped and might possibly grant you permission to record their class. Most of the time I find that dancers won't care one way or another, but there are exceptions. It better to be safe than sorry. Just think of it as a common courtesy from one dancer to another.