Comparing her to Fox News sounds like an American standpoint to me, whereas HP is British to the bone.

Rita Skeeter is the archetypical papparazzi, that are a real nuisance in the UK. It is also a stab at the British newspapers that had been following J.K. Rowling ever since the fist book became a hit and have been writing lies about her private life.

So, nope.

EDIT: Skeeter is a slang term for mosquito, which is both a reference to her Animagus insect form and to the word paparazzi, which itself is derived from an Italian word for mosquito.