That is very true, but then it comes down to independence. If the ABC is seen to be a mouthpiece for the government rather than an independent body, that only gives detractors of the ABC (from either side of the aisle) more ammo.
Again, it was probably unfortunate wording from you, so I'll give you that. I have seen idiots out there claiming the ABC is a state broadcaster in an attempt to portray it as working for the establishment (despite it being quite anti-establishment at times). Left-right distinction means nothing nowadays. At every turn, I'll correct the terminology, because the ABC is independent and thus a public/national broadcaster.