UK Politics

"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.