They would have been better concentrating on what occurred post disappearance and more specifically with Halligen and Metodo 3.
I don't think there should have been any question of the parents of a missing child being put in the situation of having to employ private detectives to carry out a police duty.
Since the police weren't looking for a live child when the case was archived and prior to that the first investigation had the bit between the teeth of investigating suspects and not a live child; with the second investigation clearing up as much mess as possible and retrieving usable information from the first; what on earth were the parents to do?
They had the money donated by well wishers ... it could have sat in a bank gathering interest when there was still interest to be accrued ... or it could have been used to actively pursue their daughter's case and what had become of her.
I don't think there is any room to criticise her parents for doing what they could to find Madeleine. I think the criticism lies in the fact they had to.