People aren't required to be interviewed by police. They have the right to refuse. If they are arrested, they have the right to refuse to be interviewed as well. Anyone, suspect or not, has the right to have a lawyer present whenever they speak to police. Actually, even if you are charged with a crime, you cannot be forced to answer questions. Your lawyer can prevent you from answering. We all know the Rs lawyers would not let them answer certain questions. However, you must answer questions asked by a Grand Jury without a lawyer present. If you refuse, you must invoke the 5th Amendment, which is pretty much an admission that you are involved in the crime in some way. And if under oath in a courtroom, you can be held in contempt if you refuse to answer questions. I believe you have the right to invoke the 5th Amendment and refuse to answer then, too, but you have to state that is the reason why you won't answer, and obviously, if you are saying you won't answer because your answer will incriminate you in the crime, well, there you go- it's like an admission of guilt.
Of course, an INNOCENT person would be anxious to be interviewed (and getting a lawyer is a prudent thing to do). Unlike the Rs who avoided it and finally, ONLY so they can say they did it, "agreed" to be interviewed.
That day, LE had the right to take the parents in for questioning, but the Rs did not have to answer.
The first sentence in the Miranda Rights, read to every person arrested, is "You have the right to remain silent".