"Screaming bloody murder" as an idiomatic expression

While reading a Michael Resnick's novel called "Old MacDonald Had a Farm", I came across an idiomatic expression that I thought was understandable in its all meanings (for that please read the last sentence of the original text below), but then I realized I could not grasp the the character's thought because it does not make any sense to me in the provided context. Can someone please explain as to what thought is hidden behind the words of that expression. Here is the text: "There’s a reason, of course," continued Cotter smoothly. "Until the international courts verified Mr. MacDonald’s patent, there was always a chance that some unscrupulous individual or even a rogue nation would try to duplicate the Butterball. For that reason, while we have shipped and sold its meat all over the world, always with the inspection and approval of the local food and health authorities, we have not allowed anyone to see or examine the animals themselves. But now that the courts have ruled in our favor, we have opened our doors to the press." Screaming bloody murder every step of the way, I thought.