I don't understand it from this angle, but to me, the general description of what they employ sounds very analogous to how noise cancelling headphones work for pilots. The noise generated by the engines, which normally would drown out any signal of humans conversing through air, is of known frequencies, and a synthesized version of that noise can be played back 180 degrees out of phase along with the original audio, cancelling the noise, revealing the signal. No one is implying that the headphones do this without sampling the engine noise, they might just not have to rely on the actual measurements in question to glean the necessary information to synthesize a signal capable of such cancellation. It reads to me like this broadband thermal noise is predictable, which is why they are able to synthesize it in the first place.
You misunderstood. I was relaying that I, too, have a decent grasp of sampling theory, and that if I understand the article's main premise, then saying they have disproven Nyquist's Theorem with this example is akin to saying that being able to draw both 30 degree and 90 degree angles with a compass disproves the idea that angle trisection is generally impossible.
They have simply shifted in time the sampling of the noise. Even if they argue they synthesize the noise in realtime, they had to have sampled it at some point to know what to synthesize in the first place. It was at this point that they were required to sample at at least 2MHz to accurately quantify their noise at 1MHz.
The mechanism used in pilot's noise cancelling headphones is much the same. they don't sample the engine noise as its being made, they synthesize it from known frequencies.
