Thanks for the correction - This still needs clarification though. I'd argue that calling it "government funded" is the better mental model and "financed by the audience it is answerable to" is giving the false impression that the audience has any influence on what they are paying for and consuming - AFAIK they don't

The BBC is publicly funded, yes. The fee is however set by the government and accepted by the parliament, in which ususally the ruling coalition (or party) holds the majority, so its effectively set by the ruling party. This does make it technically different from direct state funding but de-facto the gov still has controll over the amount of funding the BBC will receive.

So while the audience pays directly it does not have the ability to pull or increase funding in approval or disapproval but the government does.

Like you said nominally the BBC is answerable to the audience, de-facto it is answerable to the government only.

Other publicly funded broadcasters have a different system, in Germany for example the federal states decide on the licence fee.

However de-facto this doesn't change anything. Its common knowledge in Germany that the publicly funded broadcasters are quite state affiliated, there have been a couple of court rulings confirming that.

So yeah for a bigger picture looking at funding only isn't sufficient