There is sterile saline solution on the operating field and we’re taught to use it to put the fire out. It’s the most readily available thing. We don’t keep extinguishers in the OR room itself.
Typically, you aren’t talking about a large fire, so getting the fire out isn’t as important as getting it out quickly. By the time you grabbed the extinguisher and pulled the pin the patient would be burned. Whereas, the saline could be used a faction of a second after the fire is noticed, plus the water would cool the skin and hopefully minimize any burns.