Okay, then what other methods can prove that you are hearing a genuine difference?
And about downloading certain HD albums...they sound different because they are a different master! I have converted the 24-bit files to 16-bit to compare them. They sound exactly the same when you do a proper comparison.
Material and familiarity with that material is a huge part of it. If it's a (usually modern) artist with loudness problems, it's really hard to tell. I don't listen to most stuff from 2000-now because of the loudness issues. The other part is gear - if you don't have a proper DAP or digital setup to render 24bit fully, you are choking the playback.
For instance - you mentioned Linkin Park in the thread - I doubt anyone could tell 24bit vs 16bit with music like that. Most of it is fake source, or faked with ridiculous editing, and the tones are so far removed from reality of what the instrument sounds like that there's no realism to lose in the first place. There's no room, no vibe, no texture. It's bandwidth limiting pretending to be dynamic.
EDM, hip-hop, modern pop - none of it benefits from 24bit right now, because they aren't using bandwidth anyway. They are used to fitting it into 256k and making it as loud as possible, there is no reality and detail there to hear in the first place.
Go back to things recorded in the 70's, the 60's, even the 80's and into the early 90's - to me it's obvious to hear yet nearly impossible to capture. It's very easy to get your favorite zepellin or stevie wonder album at 24bit and find the used cd for $10.
There's just MORE. The amount of signal coming out the speaker, projecting the soundstage into my room - there is more of it at 24bit and thus it has more detail and more power. That is why 1.4Mbs is still > 256k and assuming it's not up sampled, 5.8Mbs is still > 1.4Mbs.
Scream mastering and remastering all you want, but everything needs to be mastered to get to it's final format, that's the definition of mastering. Whether it's been 'remixed' or not is not usually known, it's private. If the thing is a new transfer coming from an old tape it has to be a new mix, you have to bring the tape up to a proper mix -it's not a saved session file in pro-tools somewhere. so of course it's remixed.
As far as your test of bought 24bit material down sampled to 16bit, sounds valid to me. Maybe you just don't hear it. No biggie to me. You save money in the long run. Just know that it's from a combination of your material, your player, and your listening abilities, not because it doesn't exist.
I wonder, have you tried different dithers and turning dither off when you do your test? In my experience the dithers do sound different (for instance I'm not a fan of Pro-Tools' 'sound shaping' dither.