I don't understand why it would be a problem, if both parents have nothing to hide and are willing to do anything to find Lisa they should be beating down the doors of the police station asking to be interviewed.
I would want the police to be absolutely sure I wasn't involved in order to get them to focus on an intruder, NOTHING would be too much for me to do to that end.
I agree with you, especially if thats how it would go.
You want the police to know you weren't involved. They've already accused you of being involved. You've already denied it repeatedly. How will you prove a negative through the questioning? Just by repeatedly answering the same accusations with your denials? I suppose one could do that, sure.