You do not give any reference for this 'suspect' status. Which law decides who has this status and who does not? If you are just saying that anyone who wants to say they are suspects can do so, then that is probably right (though potentially libelous) but I know of no legal definable status that can be applied or removed that bears any resemblance to your concept of 'suspect'.
May i also extend my warmest welcome back Debunker.
A person suspected of potentially being involved is called a suspect in police investigations the world over.
There is no law to cover whether the police suspect someone, and indeed the suspect remains innocent until proven guilty by a court.
That suspect is still innocent until proven guilty whilst the police investigate and indeed, as in this case, after the case is shelved.
They are innocent in the eyes of the law and remain so until such time is evidence is found against them or someone else BUT that does not mean the police cannot and do not suspect they may be involved.
Don't be ridiculous about anyone being a suspect. That's plainly ludicrous. Police would suspect those with the means or the motive or the opportunity to carry out the crime.
The parents would automatically assume suspect status given they were the last to see the victim alive and well and that a high number of missing child crimes are committed by family members.
It is then the job of the police and/or the parents to provide evidence against them or for the parents to "prove their innocence" to the investigation so they can be ruled out of their enquiries.
Usually in the case of missing children the parents are only too happy to rule themselves out in order that the police may then follow other leads.