Looks like you are very 'rigorous' about others doing the work but you won't even bother digging the archive to find the links & details. Admittedly that's zero fun, but still..Read what? It’s all been taken down and Hertsens didn’t bother to link to the post describing his methods, so finding it would require scrabbling around in the archive (neither of your links have been stored on Wayback). He doesn’t say that he used the same procedure as earlier, so we’d just be making an assumption anyway. All we’re left with is a cool story.
Maybe this guy does have preternatural auditory discrimination and can resolve very subtle differences. That in itself would be interesting and definitely worth investigating further in a rigorous manner. But … no, he doesn’t bother. It’s just an anecdote that he used for a blog post, and as worthless as all the other anecdotes littering the web.
The 3amps was just one of the tests, the first and supposedly the easiest one. IIRC, there was one guy who screwed all tests but all others had good results with the 3amps. At least better than the expected 50-50. That guy was the only one who "aced" it but he was not a huge outlier, he just did a bit better. And considering how different those amps measured, the audibility claims do not seem particularly wild to me.
The cables test was the expected blalala and, also as expected, no one could reliably diff the DACs. Nothing really wild happened there.
Could that test have been done better or at least documented better? Of course! Same as (almost) any other blind test.
Does the test fail to satisfy your criteria X/Y for rigurosity? Could easily be, nothing is perfect. If you want 'total science', anything not published in a peer-reviewed journal (and actually reviewed/reproduced X times) is "anecdote". Even then it's not possible to 100% eliminate the "anecdote" part.
Just keep whatever convictions/beliefs you currently have about amps/etc and don't bother reading any of those "anecdotes". At least not until they were (re)tested for 50+ years and reached the sureness level of the theory of relativity.
Good luck & good sound while waiting...