Yes, that "warmer" sound is called "low pass filtered"...
(Real, live music has a much higher share of high frequency noise than both vinyl and CD, but it gets mastered and filtered to the tastes of the listening public.)
Since you know so much about live music, what instrument do you play?
I play keyboard, electric and acoustic six string fingerpick and steel string guitar and electric bass, Harmonica, flute, and dabble in drums. And I agree 100 percent with him.
And while we're at it, what gear do you listen on which so accurately informs you that digital is so much better.
His description is exactly what happens with vinyl. It's also similar to tube amps. We tend to like the particular distortions that we like. There are many settings in different programs that will tailor a sound to a particular style, which does depend a lot on the technology used to make them. A typical sample is an equalizer panel, say in iTunes. Assuming no distortion in any other part of the system, there would be no need for anything other than "flat". In fact, in a perfect system, any adjustment is just adding distortion.
But we don't hear like that. I do love the sound of tube amps. But I'm not so conceited as to declare that the best. You can listen to Rameau with hip hop filtering on your system as far as I care - it's what you like.
DIstortion is even desirable at times. Guitar on an overdriven tube amp makes for a very interesting sound.
But to the subject at hand, it isn't difficult to prove that digital has much higher potential for much less distortion compared to vinyl or tube amps. It's all just that some people prefer the distortin that they like.
Note: a lot of CD music these days is coming out with a lot of distortion and compression in the original mix.