You've probably already figured this out already, but this is total bunk. No instructor makes his students swear an oath not to reveal who taught them. Even if you managed to find one paranoid teacher with such a rule, I can't imagine finding two in a single lifetime.He claims to have taken an Oath not to reveal Both his Kenpo teacher and his Wing Chun teacher.
Now it's possible the guy swore an oath to himself not to tell anybody that info. If so, it's probably for some reason like a falling out with his former instructors, he learned from videos, he lied about his rank, etc..