No - if you make the funding independent from taxes then it doesn't have to be in favour of the government.
The German publicly funded journalism is a mandatory payment by everyone unrelated to their taxes (which makes it a favourite target for right wing people claiming it's unfair because it's too liberal for their taste when it's literally the definition of fact and science based centrist reporting)
The are often critical with the government and not propaganda at all.
In Europe, we have public services news organizations, that are still independent. While not perfect, they're more independent from their state than most newspapers are from their shareholders. You can read more about Arte, the European public service channel dedicated to culture