Let us remember that the chase after Montag is being broadcast live onto television, to create a real life entertainment slot that is designed to thrill and titilate the attention of the viewers in this media-obsessed society. When Montag actually manages to fool the Mechanical Hound and lose his pursuers, they cannot actually admit this on screen, as to do so would make very bad television. This actually works to Montag's favour of course, as after his "death" he is free to go and do what he wants to do. Note how Granger explains the irony of what they are watching on television:
They're faking. You threw them off at the river. They can't admit it. They know they can hold their audience only so long. The show's got to have a snap ending, quick!
In reality, the irony is based on the fact that the government is a victim of its own success. Having promoted the media into playing such a key role in the lives of its citizens, it now needs to obey the rules of that media and give its audience the kind of dramatic ending they have come to expect, whether or not it is factual.