This well known result does not contradict my claim. Neither of the examples of possible consistent market beaters I mentioned run managed mutual funds and I would not expect to find many such people running managed mutual funds. I would expect them to mostly be running hedge funds (like Hendry), investing for themselves or using regular companies as investment vehicles (a la Buffet).

Even with actively managed mutual funds the evidence you present does not directly contradict the possibility of genuinely skilled management. There is strong evidence that actively managed funds do not outperform the market on average and fairly strong evidence that past performance is a weak predictor of future performance (suggesting luck more than skill is the explanation for outperforming benchmarks in most cases) but the data does not rule out true alpha in the tails of the distribution. In fact, I just found that Fama and French are explicit about evidence for this existing:

If we add back the costs in fund expense ratios, there is evidence of inferior and superior performance (nonzero true α) in the extreme tails of the cross-section of mutual fund α estimates.