Of course, you could just say 'Who said ...' but then that doesn't show that the speaker thinks s/he knows the answer or at least that s/he know that s/he is quoting someone.
If you look at the answer, 'it was X who said that', you can see which part of the sentence the question is about and why there has to be 2 'who's. ( 'who' the question and 'who' the relative pronoun)