Trump: I moved on her, actually. You know, she was down on Palm Beach. I moved on her, and I failed. I’ll admit it.
Unknown: Whoa.
Trump: I did try and fuck her. She was married.
Unknown: That’s huge news.
Trump: No, no, Nancy. No, this was [unintelligible] — and I moved on her very heavily. In fact, I took her out furniture shopping.
She wanted to get some furniture. I said, “I’ll show you where they have some nice furniture.” I took her out furniture —
I moved on her like a bitch. But I couldn’t get there. And she was married.
And when you’re a star, they let you do it. You can do anything.
(Man) Whatever you want.
Trump: Grab ’em by the pussy. You can do anything.
Knowing that women don't let him do that might might be a good reason to put words in Trump's mouth and remove "they'll let you" from his sentence, but it is not a faithful translation.
What he said was that they let you do that. It's not true that the women let him do that, but that's what was uttered. As a translator, you don't get to change what someone said, to instead match the truth that you learn from somewhere else.
For an example, a famous lie is that Nixon said "I am not a crook." We know he was a criminal who resigned due to his criminal activities. So can I change that line from "I am not a crook" to, "Nixon called himself a crook"? After all the reason for his statement or the use of the word crook was the fact that he was a crook, and making a public address on this subject.
Of course not. And likewise it's wrong to change "they let you grab 'em by the pussy" to "grab 'em by the pussy" by misquoting the sentence. It's there in black and white, you just have to read it.