if the history doesn't matter to you then that is fine. It is good that you are happy with what you are learning, and ultimately that is all that matters.
But doesn't honesty and integrety count for anything? All the signs point to the "Da Sifu" being a liar, plain and simple. What he teaches may be pretty good, but personally I wouldn't want to be around something like that. In the martial arts, the students tend to look up to their teacher like a young child would a parent, or how a religious person would their priest. Now, if a teacher is dishonest enough to lie to the public about their background in order to gain more students, then odds are that lack of moral character is going to bleed through in other ways too. Usually this results in a cult like defence of their teacher no matter what, not wanting to believe they've been taken for suckers, or this man/woman that they look up to could be this dishonest. In the end they become liars too, whether they realize it or not.