You are correct about it intentionally being silly, but not about who it was lampooning.

The idea for the song came about when the Fairbrass brothers were running a gym in London where, according to Richard, there was “lots of narcissism and posing”. One day, he took his shirt off and started singing “I’m too sexy for my shirt” in front of a mirror as a joke. The band originally recorded it as an indie rock song.

https://en.wikipedia.org/wiki/I'm_Too_Sexy

So basically it was just a comment on narcissism that got completely misunderstood.

Sort of like how Born in the U.S.A. is the opposite of a patriotic song.