This appears to be a good comparison between the real footage and the BBC edit:
IMO the BBC programme ‘Panorama’ (a documentary series) did a perfectly factual job of reporting the event. The extra words that were removed in the edited version don’t change what he intended to convey, as exemplified by what followed and his lack of presence there despite his promise.
Hypothetical: If he had used incitement wording and then walked it back and admitted the problematic nature of his wording (during the same speech) and combined it with his continued presence with the crowd at the Capitol where he continued to defuse the situation, then the BBC posted his comments in the manner in which they actually did after a hypothetically completely peaceful day of protests, then I would completely agree that the BBC were at fault.
Trump’s tactic in that speech was quite similar Charlie Kirk’s tactic, as seen in this breakdown:
“They’re taking him out of context!” How often have you heard that defense? What if the “context” is just more manipulation? This video is a crash course…
(TLDW: Inflammatory dog whistle immediately immediately followed with a softening of that statement, then rationalise the original statement and double down)