Celebrity Skin

Pardon me if you've seen this point elsewhere, but in what sense is John McCain not a celebrity? I've seen him on the covers of magazines, on television, in newspapers, doing guest appearances on SNL, etc.:

Could you possibly be a major party presidential nominee and not be a celebrity? But in particular, McCain actually stands out among politicians as being someone who was a famous celebrity first and then parlayed his fame into a political career, rather than merely being someone who's well-known for being an important politician.