You can have a copyrighted derivative of a copyrighted subject - for example, buying a stock photo of the eiffel tower at night pays both the photographer and the lighting designer; and buying a translated book pays both the original author and the translator. This is known as a "derivative work".
However, to be copyrightable as a derivative, work must contain sufficient new expression to satisfy copyright law's requirement of originality. So you can't copyright a photocopy of a book, for example.
Presumably Genius thinks their lyrics are analogous to the photograph, rather than the photocopy; they may not own the lyrics, but they own this particular transcription of the lyrics.
Pretty sure that's the main reason Genius will have difficulty pursuing this case. Google isn't infringing their copyright, because they can't copyright someone else's work, and I doubt the unique pattern of apostrophes is enough of an infringement to claim Google stole, it merely proves the source of the content was them.
It does, at the least, suggest Google is paying someone who less than ethically sources their data though.
Copyrights, patents, and trademarks have clear limits. An overly expansive theory of copyright would be stifling to innovation and free expression.
It was sourced from someone who was liberal about taking legal risks, but I have a hard time seeing what ethical rights were broken. Indeed, the opposite theory is that if we don't exercise out rights, they go away and Google's source is risking litigation to preserve our rights.
The rightsholder here are the artists and their proxies (publishers and agents), not Genius. I wouldn't feel bad of they asked for a takedown or royalties.
However, to be copyrightable as a derivative, work must contain sufficient new expression to satisfy copyright law's requirement of originality. So you can't copyright a photocopy of a book, for example.
Presumably Genius thinks their lyrics are analogous to the photograph, rather than the photocopy; they may not own the lyrics, but they own this particular transcription of the lyrics.