As I said, I'm not a metallurgist but I did take several metallurgy classes as part of my formal education. Part of my study involved annealing and studying cartridge brass. I know how it works. And although I don't routinely measure the hardness of my brass or spend hours polishing and acid etching samples to study under the microscope like I did in the past, I have a pretty fair idea of the results of my particular annealing process when comes to the metallurgical properties of cartridge brass. It has nothing to do with what I WANT to believe. Annealing cartridge brass is well understood science.
What you seem to have missed is that both Mr. Lutz and I are unable to prove is how annealing affects, positively or negatively, the group size of a representative batch of rounds fired at a target 100 yards away. But being unable to prove something is not a final answer, one way or the other.
I don't know how Mr. Lutz feels about annealing after his short experiment but I happen to believe that annealing every time is one small step of many which helps me make ammo good enough to win matches. If I had to choose among three results, those being annealing hurts a little bit, annealing can't possibly make any difference, and annealing is likely help a little bit, I would select the last one, especially since I know something about how annealing works. It makes sense to me that annealing should help even if only to a small degree. It doesn't make sense to me that wearing lucky underwear is more effective than annealing. I happen to believe that one is science and the other is a myth. Others may disagree.
The statistical noise inherent in the way most of us test ammo makes it impossible to quantify the effect of a single small step, uniforming primer pockets for example. But that doesn't mean that uniforming primer pockets isn't worthwhile when combined with annealing, bullet sorting, and so-on.
Your post disagrees with this idea. Please explain how you can apply scientific testing methods to the process of annealing cartridges and prove or disprove the effectiveness of annealing without involving shooting.