You shouldn't have to worry about fire when broiling. You might get an occasional poof of flame when the product spits directly on the heat source, but it shouldn't actually be any sort of a fire hazard.
I broil often with many different meats and fish, and quite often I will lightly paint the cuts with oil (olive or vegetable, depending on what I think works best
).... It both helps the food retain moisture and cook better, but it also helps to hold the herbs and seasonings on the meat while it's cooking. I've never had any sort of fire, even when accidentally overcooking something.