They have the equipment and muscle power to move people. What are a couple of EMTs going to do with a 600 lb guy on the third floor of an apartment building, or someone trapped in a smashed car?
Those seem like more edge cases (most people don't weigh 600 lbs and most car accidents are minor collisions with little to no fire danger). That doesn't justify the extra expense of using them in other situations like the ones mentioned in the article which could easily be handled by police and EMTs.
Right... and it's going to take that guy an extra five minutes to get to the hospital.
They can't depend on what people tell them on the 911 call. The average person is completely unreliable under stress.
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).