It can verified, but in order for that to prove that he didn't misrepresent himself requires you to believe that a. he has an "actual" race that he can lie about and b. to believe that his "actual" race is determined by whether people treat him as black or not. Those are some pretty big assumptions and this uncertainty is while shitheads like Milos can still say "see? I wasn't wrong".
But that kind of delusional "uncertainty" exists for everything. The "uncertainty" regarding the existence of evolution can lead some people to question almost everything about biology. Is it worth anyone's time considering this or what those kinds of people have to say or how they justify it? Absolutely not. Irrational hatred and ignorance will find a way.