British sniffer dogs
I think the assumption is that the body was disposed of while the McCann's were doing their tour of Europe. This obviously would mean other members of their group, who were there in Praia da Luz while the McCann's visited the Vatican, would fall under suspicion as well.
To do all of this they would have needed someone with local knowledge to assist them, Murat possibly.
But it is true to say that when their tour was underway the spotlight was most definitely on them not on their friends/relatives back in Portugal.
Perhaps even it's not too much of a leap to make to suggest that the McCann's haven't been told where the body was disposed of in case they were asked to take a lie detector.
In any event it's very strange that in a police interview they would both stonewall a lot of questions or the equivalent of "pleading the 5th" as the Americans call it, which is normally done so as not to incriminate themselves.