This is totally false. Mastering is very important – however, the quality of a track starts at the performance and the song. The sound quality starts at the tracking. A well tracked recording is easy to mix – you’d really have to go out of your way to make it sound bad. That being said, great mixing can take a great recording to amazing places, or at least take a decent recording and make it sound good. If you wait until the mastering phase to look for quality, the mastering engineer will be doing her/his best to make the record listenable at all.