https://en.wikipedia.org/wiki/Distortion#Harmonic_distortion
As the word "distortion" in that link implies, where audiophiles go wrong is confusing "nicer" with "better."
70s dub-reggae records and the like would undoubtably sound worse if they were recorded straight to digital and pressed to CD. Similarly, lots of 21st century music would lose its edge if it were printed to tape and pressed to vinyl.
Most of this confusion stems from audiophiles borrowing terms and ideas from music engineers and artists, much like the neverending stream of badness from managers/MBAs taking ideas and terms they don't understand from engineers.
If you are listening to music, it is none of your business to decide that it needs to be "warmer." The people who made the record spent a lot of time and effort making it exactly as warm as they wanted it to be. Pushing it through a tube amp to make it warmer before you listen to it is like retouching a Monet print in photoshop before you hang it on your wall. As you can imagine, I'm not a fan of the EQ settings on ipods either.
When optimising your playback system, go for maximum transparency, and stop there. If you don't like how the record sounds, listen to better records.
If you're making records OTOH, it is entirely proper for you to be worrying endlessly about "warmth". Buy up crazy 70s gear from ebay, have the track pressed to 60g vinyl at a boutique german cutting house, whatever it takes. Warmth is tricky :)