Quantum randomness, on the other hand, is real randomness
I'm sure that there is a mathematical proof of this somewhere (not that I'd be able to understand the maths) but is it really true? Lots of stuff have been assumed to be really random that later have been found not to be once we understand or model the underlying mechanism.
So, since we don't really understand quantum physics terribly well at the moment, how can we be confident that the statement is true?