Senoufou, I have heard of trials being moved to a new district because of adverse publicity close to the crime site. This is called change of venue. But I have never heard of anybody getting out of being tried because of publicity.

However, in the case of the Madeleine McCann abduction, it would be hard to find anywhere in the western world where there hasn't been plenty of publicity.   

Now that I think about it, I doubt that mere publicity is enough of a factor. The last case I can think of in my region where there was change of venue was the trial of a woman whose two Rottweiler dogs killed a ten-year-old boy. Neighbors had been complaining about the dogs, and people had asked her to control them, and she had not. She wasn't just the object of publicity; the whole populace was in flames against her. The trial was moved maybe 150 miles west.
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About court cases in general: I read a good sentence years ago in a book about the Watergate scandal under Richard Nixon. When the burglars appealed their convictions, the appeals judge wrote, "The defendants are entitled to a fair trial, not a perfect one."