The reason a fire engine responds to a medical call is due to the type of 911 system that we have here in Clackamas County (and it is the same in Washington and Multnomah County). This system puts a fire engine and an ambulance in route to a medical call for the safety of the citizens. Generally, this will get more than one paramedic on scene to provide patient care. Also, many times calls require additional manpower. This means that if someone needs to be carried out of their home or their condition worsens, there are plenty of people there to help- as opposed to calling for more and having to wait longer for assistance.
Another reason that a fire engine is called along with an ambulance is that there is always more fire engines working than there are ambulances at any given time. This makes for a much quicker response when seconds count.