It is, the government can not prevent or punish people speaking on the basis that the government decides it was misleading.
A civil dispute between private parties is entirely different though. One can be found liable for misleading speech that causes damage to another party.
> The president is trying to throw his weight around because he thinks his fans will like it. He's an idiot.
Aside, using civil courts to attack opponents is certainly a problem, but in USA it favors the speaker a compared to a lot of other countries. In US the plaintiff has to prove the speech is false and for public figures that there was malice. Which in my opinion goes a bit too far and gives media corporations more power over politicians and other public matters. I think the public figure stipulation is reasonable and important to allow private citizens to discuss politicians and public matters so that's good, but I think there should be a counter to that which requires organizations reporting the news to have more duty to report truth and not mislead.
Is clipping a video together to create a lie "speech"?
The BBC admitted a mistake. The error was reported by an internal BBC investigation, not because Trump's team complained (it is highly unlikely they saw it originally, because it was an UK broadcast).
The BBC makes thousands of hours of video annually. You can't expect perfection, or to sue them for billions of $CURRENCY for every mistake.
The mistake in this case was to make their quite reasonable case (that Trump encouraged the violence of January 2021) very slightly more emphatically than was perhaps justified.
Trump of course showed his disapproval of the violence by pardoning all the rioters, including those convicted of injuring police with weapons.
Is it protected if you are challenging a UK company in the UK?
If he sues in Britain, then it will be run under British law.