It seems that "Explain your answer" is semantically pretty close to "Why" so I can understand why the student wrote "because." However, "she said that..." doesn't really give the reason why, as the answer "Because she had something to hide" would.
I don't really understand the purpose of "Explain your answer." Are you trying to force them to use reported speech? If you're trying to just check the information, "How do you know?" might be better. As it is, I find it a bit confusing.