I think she actually did squeeze the היא in there. Between her speed of speaking, the fact that ה is often not pronounced by Israelis, and the fact that the word preceding היא ends in the same vowel, the result is that you can't hear it at all.
They are going for the intransitive. So how would you phrase a question about the identity of this other person such that the two of them are hugging? ISTM that the right way is either the given answer or "With whom is she hugging?"
I agree that it's tortured, but the Hebrew is intransitive (otherwise it would be "את מי היא מחבקת").
You need this formulation of English to convey the same meaning. This is true even though an English-speaker would avoid the sentence and say something else instead. The meanings are not equivalent.