The thing is that the value in this case is not in the lyrics themselves but in the transcription and compilation into a central database. The people looking them up already have a copy - they are listening to the song. A transcription is something they could do themselves if they wanted to put in the effort.

From a maximalist perspective you are quite correct. But from the perspective of how much the publication affects the market for the lyrics I think it is reasonable to conclude that at worst the impact is marginal and in the vast majority of cases it has none at all.