Tradition in the Martial Arts
Each martial art style is part of a family of martial arts that share a common rooting system. This rooting system is based on similar traditions, origin and history.
It takes a lifetime of dedicated training, development, and interspection to become a true master of an art. For any person to claim that they've mastered multiple martial arts is at the very least suspicious and at most fradulent. This same rooting system pays respects to the founders of a particular style. Oriental tradition in general pays great respect to one's ancestors and elders. It is for the same reason that while it's okay to experiment in varied styles, it is frowned upon for an instructor to claim multiple backgrounds, as it shows a lack of respect for his teacher and the art itself. Much like a child who cannot have two biological fathers.
While many martial artists today have a theoretical understanding gained through varied resources available, such as books, internet, movies, etc., a true understanding of an art and of combat can only be gained through experience. As with many things in life, actions speak louder than words. A student should not listen to a prospective instructor, but rather observe his abilities.