A double blind test is a kind of experiment; if it's independently verified, then it's science. I doubt there's a case where a group could hear a difference (scientifically demonstrated) and a difference could not be measured. It seems more likely that one of the following would be true:

• A difference is clearly measurable but it's not immediately clear which component(s) of the difference are audible
• A difference is clearly measurable but the difference doesn't make the test subjects or test administrators happy

The former explains the cases where something "sounds better" although it has "similar" specs. We aren't looking closely enough at the measured differences, and companies like Harmon Intl. use this as a means of making real useful progress in understanding what matters.

One example of the latter was a test where (sure enough) tube lovers could identify and prefer the sound of tube amps and the measurable difference was (drum roll) the tube amps in question had slight (but barely audible) levels of even order harmonic distortion. This apparently meant that that group of listeners preferred the sound of a little distortion, which, needless to say, didn't sit well within the group itself.

The limits of human hearing are, at an extreme level, set by the physics of pressure wave propagation, diameters of the atoms involved and the 'sound pressure' produced by Brownian motion. Measurements in the electrical domain prior to the transducer suffer no such limits and may be orders of magnitude more precise.

If humans could hear much better, we could hear how warm the room was. Not very useful.