

I don’t place much stock in anonymous complaints. There are many examples of bias in Palestine’s favour, too. The most recent example is the Gaza documentary, funded by the BBC. It was so biased that the BBC had to apologise and remove the documentary. They literally gave money to Hamas. In the translations, all mentions of the word “Jews” were translated to “Israelis” or “Israeli forces,” and all mentions of “Jihad” were translated to “battle” or “resistance.” For example, one woman interviewed stated "Sinwar was engaging in resistance and jihad against the Jews,” but the subtitles read “he was fighting and resisting Israeli forces.”
The nature of very large organisations with international presence is that there are many people with many different political beliefs all under one umbrella. In the last few decades, journalism has tended to attract many more left wing people. It would not surprise me that more BBC employees wanted a left wing bias on reporting, and perceived objective journalism as biased.
“Incorrectly” is a judgement. It is a judgement that the statement is false. To illustrate the issue, let’s use your example: “X incorrectly states that the sky is yellow”. Let’s imagine that the BBC writes, “Trump incorrectly states that the sky is yellow.” Trump and supporters reply, “but the sky is yellow during certain atmospheric events common in the morning and evening. Here is a picture of a yellow sky.” Now the BBC is caught defending a truism which is, in fact, not always true. Supporters of Trump can rightly point out the BBC’s inaccuracy, and would likely consider it a form of bias and partisanship. In order for the BBC to avoid this, they would need to append a long legal disclaimer at the bottom of every headline, every article, every video, and every news report, thoroughly detailing the various ways in which the judgement could be interpreted, how and why the BBC came to that judgement, their peer reviewed citations and statistics, the background of the analyst who made the judgement to ensure that they aren’t biased, etc. This still wouldn’t be enough, because Trump supporters would then ask, “but why didn’t you write an article about all those times Kamala Harris lied about Biden’s mental acuity? You didn’t use the word “lie” even though she clearly lied.” They’d be right. Now the BBC has opened themselves up for criticism of instances in which they didn’t editorialise.
Judgements, no matter how factually correct, are judgements. They lead to a race to the bottom. I don’t see how you could look at American media and argue that that is what the BBC should do.