The government, when it can't find Montag as he is on the run after he kills Beatty, claims they have found him but it is really just some guy who slightly resembles Montag. The reason they do this is because it would not look good on them to appear to lose their quest. It is important to them to appear to be completely in control and completely victorious. If they failed to catch Montag that would show them to be vulnerable and not invincible. They believe that they must keep people happy and they believe that a vulnerable government would make people unhappy and show that the government has flaws. The society of the story is one in which the government has taken on the duty of telling people what to do and what to think - they are the keepers of the people and, as such, they are like parents to little children. If little children see their parents fail at something, it often scares the children because it lets them see that they aren't completely safe. The people of the story's society are those little children and if they saw their government fail, it would frighten them because they do not think for themselves any longer. The government, in its Big Brother role, must make the people feel secure and make itself look invulnerable so it finds a substitute for Montag and makes itself then look victorious.
The police knowingly pursue a man they know is not Montag. The media knowingly broadcasts the pursuit and capture of a man they know is not Montag. Though the actual capture of Montag is important, what is of greater necessity is presenting the state in action. The citizens must know that the government is watching and will pursue those who violate the repressive laws that are in place. The pursuit and capture of Montag's substitute is an example of the consequences. It doesn't really matter if it is Montag or not. The example is all.
This pursuit symbolizes the manipulation that the state uses on the citizens. They portray what they want them to think, rather than what has occurred. The are creating the reality that they want the people to live in and respond to. As TV has become a virtual reality, so the news has become a virtual reality.
This is epitomizes the maxim that one does not respond only to his own reality, but even more so to the reality as seen by others.