I certainly cannot verify the fact whether Mao is a Hakka, but I do believe the news script is not a fake. We do need more evidence to confirm it. Mao grew up in Hunan so he probably did not speak Hakka any more. But the fact that he did not speak Hakka and might not even know or care if he was Hakka should not exclude him as a Hakka decendent. One interesting thing I would like to bring up is associating Hakka with either all the virtues or vices would get ourselves trapped.
History is history.
We should leave history alone. Evaluation of Mao is not the point here, but let us be objective that there are angels and villants among Hakkas too.