The problem is that the reported subjective experience is almost always directly linked to technical specifications like 24/196. And that IS very probably a false claim, as it is very probable that the experience has really nothing to do with those specifications. If someone claims that 24/196 sounds better than 16/44 to him/her, it's not the actual sound format that causes the subjectively different experience but the persons limited comprehension and prejudices about those formats. To put it differently - if a person claims that 24/196 sounds better, he or she is very probably just plain wrong. It's his own mind that causes the subjective difference, which, of course is very real. But the claim itself is fallacious.
"24/196 sounds best to me" - it's just not true - prejudices, the lack of understanding of basic digital audio principles and human hearing limitations, is what causes 24/196 to subjectively sound the best. I can easily live with a claim that "24/192 sounds best to me, but i don't really know why". That's fine, you can't obviously know everything about everything. Bigger numbers, peer pressure, obviously it's usually going to sound better if you don't know the underlying facts. But not knowing stuff doesn't make an incorrect claim true. And that, of course, is the very essential reason why we need objective confirmation when talking about technical specifications, because as technical specifications are not subjective, it is wrong to link subjective impressions to objective parameters without objective confirmation.