OMG, I know this is like trying to talk to a stump, or beating a dead horse, but seriously this argument is flawed on MANY levels.
First off, the very word "
Analog" was chosen originally (back before digital computers existed) because it was a representation of the original.  At that time, NOBODY argued that a recording was an exact copy of the original.  In fact they acknowledged that vinyl was a pretty flawed medium and then went about finding ways to get around its flaws.  For example, ever hear of the 
RIAA Curve?  That is an equalization curve that is used because the vinyl record is not capable of accurately recording low frequency tones (without destroying higher tones) -- so they are reduced when the record is cut, and emphasized when played back by the preamplifier.  And of course, die-hard vinyl fans turn their ears off to the ever-present snap/crackle/pop due to dirt, or bad needles, or the "wow" introduced by the slightest warp of the media, and the vastly lower dynamic range.  And they completely ignore the fact that each playing of this magical vinyl "analog" damages it, making it less and less accurate.
Yeah, vinyl records are superior to digital recordings -- go pull the other one.
But I fully accept that vinyl is preferred by some exactly because of the distortions (called "warmth" in the analog community) it introduces.  That's fine -- that's a matter of opinion.  But to state this as fact is simply wrong.
PS:  And just in case you are still hung up on discrete samples vs. continuous, read up on the 
Nyquist Theorem.