I believe that Hotel California is still under protection as a melody, rather than a performance. Hence covers require either a license or fair use according to law. This differs a lot from the case of performing a 200 year old song whose melody is in the public domain.

Not to say it was wrong what you did, or that Google was in the right for flagging. But Google was legally correct.

(Google suggests controversy around the question of whether hotel California is public domain or not)