The more I read of this, the more it seems like the OP is asking for someone to provide “proof” that a relatively poorly performing DAC cannot beat an excellently performing one in some sort of competition. If people here are saying “they sound the same in real-world situations” then a red-zone DAC is just as good as a blue-zone DAC if you’re listening to them side by side. I think this demonstrates a misunderstanding about what we’re doing here.
First, the rankings here, unlike in the magazines we’re used to reading, are not intended to show some sort of sound quality hierarchy, but instead show differences in quality of engineering. I don’t wish to speak on behalf of this forum, but it seems clear that the DACs that are recommended in the reviews are recommended because they demonstrate a well-made product, not a superior sounding one. Although it’s likely that the worst-engineered DACs on the list will alter the sound of whatever is played through them, that doesn’t seem to be the point.
Therefore, the people who buy a magazine’s recommended product because it supposedly sounds better are going to be led astray trying to follow the same logic on this site. People who subscribe to the sort of thinking common on this forum are not claiming the blue zone DACs *sound* the best, but instead that they demonstrate the best technical skill in their execution. When people on other forums say, “how can those ASR people claim that DAC A beats DAC B when they also say they don’t hear a difference?” they are making an apples-to-oranges comparison. What they’re doing is not what is being done on this forum.
Back to the original question, can we prove that a blue-zone DAC can’t ever be be beaten by a lower-zone DAC in a listening test (even a well-executed test)? No. Most will sound the same. But we’re not making that claim—that is a different way of thinking.
Edit: comments above refer to DACs only. Amplifiers are probably a different story and speakers certainly are.