The example you give about metal fans and Bieber is a perfect example of No True Scotsman. The term "metal fan" will be widely understood to mean "someone who likes metal music," not "someone who never listens to anything other than metal music." The initial claim is clearly false, so the person revises the claim to contain the word "true," which reduces the argument to nothing more than "well I refuse to consider you a metal fan if you listen to Bieber."