I get your point, but that's just editing text and I did not "say" those words, but typed them - the BBC was broadcasting parts of Trump's speech, so it is literally his words. Also, that's a lot more editing with your example and doesn't entirely make sense without the "not" - there's also the argument that deliberately leaving out negations is a malicious attempt to change the meaning.

The BBC editing was "merely" snipping out a bit in the middle - likely due to time constraints. I don't agree with their editing, but it's not in the same ballpark as your example.

Incidentally, I have previously raised a complaint with the BBC for one of their news articles when they edited a bike cam video by snipping out a bit in the middle. The removed part showed an aggressive driver performing a dangerous close pass on a group of cyclists, so without that, it made it look like the cyclists were hassling the driver for no reason.