Why is this man keeping it a secret where Madeleine's body is buried? Why doesn't he speak up and end the torment for the parents? Isn't he supposed to have given his theory to the Portuguese Police? Why haven't they said or done something about it? Hmmm I wonder.
If you read the book (which was a particularly painful experience as it is self-edited), and I think we should all read the various volumes on the case for balance, he has contacted the family via email several times. He's also contacted the PJ, Amaral and Wolters.
Is there a secret place? Well according to the book, Madeleine is buried in scrubland near the overlook at Rocha Negra. He apparently convinced the PJ to conduct GPR surveys and had a go at excavating one of his likely burial sites, both to no avail.
It seems a very unlikely disposal site in my opinion, as it would obviously require running the unnecessary risk of transporting a corpse over a kilometre and digging a sufficiently deep hole.
Quite why he hasn't followed through on his assertion that he intends to enlist the services of a South African EVRD team, is the subject of some conjecture, as this would resolve the matter within hal an hour.