The original article claimed that "of necessity [lossy codecs] eliminate some of the musical information". I don't know how to quantify the musical information, but given another statement that "[l]ess bits always equals less music", it seems to be more or less same to the information-theoretic complexity. But as you have correctly guessed, there are a lot of places where the information can be lost, everything from performer's skills, musical instruments, ADC/DAC processes, and up to speakers. So "information not lost" is not a good argument for bashing lossy codecs, because you have lost so many informations already, just that you haven't noticed yet.

Also I claim the lossless compression exists even after this massive reduction of potential information because you can prove that a specific step is indeed bijective. In fact, even the most of lossy codecs are lossless. They are designed to lose some information at the very specific point so that they can be analyzed. "Lossless JPEG (re)compression" wouldn't make sense unless you realize that those lossless steps can be done more efficiently. I have seen enough people who assumed that this is impossible though...