You and I probably agree that Trump didn’t get to say what he actually wanted to say. I assert those two lines come closest. The attentive watcher might see the cut (two different camera angles) and put in the effort to watch the 50 min. in between. But biased people would just presume it fits a pattern.
That's irrelevant in the context of a supposedly reputable news source reporting on what he said.
What BBC did was literally make fake news, something they and other news outlets are accused of doing oh-so often these days.
If they wanted to publish what Trump "actually wanted to say", they should have done that the proper way by finding some third party, like a political expert or similar, which could analyze the speech and convey what Trump "actually wanted to say".
Do you think Trump is being taken out of context?