Re: In spite of/Despite me telling her Yes - I think the book was badly edited and they've missed out a part of the explanation, which should have read much as I said above :
If, on the other hand, the subject of the two verbs is different, then the "new" subject must be inserted.
She paid for the meal. John told her not to.
She paid for the meal despite John telling her not to.
If the subject can be reduced to a pronoun then either the object or possessive pronoun can be used :
John said that she paid for the meal despite his telling her not to.
John said that she insisted on paying despite him telling her not to.
So in your example, this would become...
She paid for the meal despite me/my telling her not to. |