Of course, he has said the "N-word". People might not like her, but she isn't stupid. She wouldn't have said publicly if it wasn't is verifiable, and since Omarosa was interviewed by Mueller, Mueller probably has the original tapes.
She has been a Trump associate since 2003 and knows he is a pathological liar. Just like his lawyer, she felt that she needed evidence of what he said if he tried to blame her for one of his scams.
Trump has a limited vocabulary but his racial epitaph is enormous. His former associates and employees have said that he despises four groups of people the poor, women, Blacks and Mexicans. Everyone knows that.