To clarify:

What's wrong with any hardware RNG that produces 0's and 1's straight from observing natural phenomena like "thermal noise, the photoelectric effect, and other quantum phenomena", as wikipedia puts it[1].

How can they do better than that; specifically, what do they mean with "demonstrably unpredictable values"?

[1] http://en.wikipedia.org/wiki/Hardware_random_number_generato...

From the quote you already posted: "in any classical physical context". They're not talking about anything quantum.

Got it, thanks!