they used the media to confuse things putting out stories that were untrue from the first night, they were not out looking for their kid bit phonjng dozens of people in the uk who then went to the media, then it snowballed and no one knew what was true or false, a perfect hiding placeI agree in general, but there have been so many cases where the parents did everything they could to expose the case to the media after faking an abduction. It doesn't usually go on for 5+ years, of course, but it happens. I'm thinking of the Shannon Matthews case in the UK, or the Susan Smith case in the US. In the extreme, there's the JonBenet Ramsey case; her father recently published another book 16 years after the child's death.
eg
They spread the story that night that their window shutters were forced, broken, smashed, when it just was not true
They also spread the story about police being useless too and blaming them for things they had actually done ie trash the apartment
they also LIED about when they called the police, they did not call them until 10 40 pm this is logged by
Olice and can be found in the police files as opposed to kate saying it was within 10 mins of 10 pmand then complained that police lost the golden hour when this did not exist as the golden hour is an hour from when a child is last seen which was 9 15 according to the father, another lie and slur on the portuguese police