Actually that's the thing which first made me question the narrative.

In the speech he clearly says "they're bringing ... their rapists" not "they're [all] rapists" but every news source, even supposedly unbiased news programmes like the BBC, were reporting against the facts and clearly editing the video to make it worse.

He clearly says something along the lines of "When Mexico sends its people, they're not sending their best. They're not sending you. They're not sending you. They're sending people that have lots of problems, and they're bringing those problems with us. They're bringing drugs, they're bringing crime, their rapists. And some, I assume, are good people." You have to really force your ears to hear something different. The trouble is Trump doesn't speak in a normal grammatical way. He goes off on tangent, leaves points then goes back to them so it leaves him open to this kind of dishonesty editing.