This society cannot allow a dissident to escape. In order to preserve the society they had to have an end to the chase so they found some innocent soul to take his place. It would not be fitting to the members of this society if Montag got away, it would destroy their simulated contentedness. In order to keep the members of the society content and calm, they must think that the chase ended with the successful capture and death of the dissident Montag and an innocent scapegoat had to take the fall.
Also, since it was televized, the government must assume that their are people watching this in their homes, and cannot continue a long and winding chase and satisfy them with a short chase. A long chase would mean that the government cannot finish off a fugitive, and that would mean that they can't control every part of society, which would make them "lose face". Going back to the televized part, the government knows their citizens have short attention spans, and therefore wishes to make them happy with a short and definite ending.