You've got to draw the line somewhere. There's always situations where having more people/resources would have made the difference between life and death. In an ideal world, you've have a fire station on every block, dedicated traffic lanes just for emergency vehicles and you'd use a helicopter to get someone to the hospital as quickly as possible when it might be slightly quicker than regular ambulance transit.
It just not reasonable to use that many resources in 1 in a million scenarios like you are mentioning (where a 1-2 police officers and 2 EMTs couldn't handle the situation, the person calling couldn't provide enough information to determine whether fire fighters were needed and making it to the hospital 5 minutes sooner would have made a significant difference in the outcome of the victim)
Per the article, only 1.5% of the incidents the SFFD responded to involved fires and they had a budget of 330 million dollars. How much money could be saved by using police and EMTs in those situations? (and used in more effective programs that are actually going to help the homeless get off the street).