I like the concept of the triangle. And agree for the most part, but also remember that you do not need to fight every leg of the triangle to put out the fire. If you remove the fuel, air, heat or can interrupt the chemical reaction that is causing the fire, then you might put it out.
It also depends on what is burning and the size of the fire. If you have a fire involving something like calcium hypochlorite (pool chlorine), you will probaly need to just get away. It will supply oxygen to a fire from it's decomposition, which accelerates with heat. Or if it can be handled with water or an extinguisher or something, do that.
The situation you are faced with might be able to be handled by any one of the corners of Blast's triangle or by a combination or two or maybe all three. We are more prepared when we have all three corners available to us, but how frequent are those times?
And there is one more thing to add, and it really is jsut adding to the resourcefulness comments, THE ABILITY TO KEEP YOUR HEAD AND ACT.
When I was in grad school, I put out a car fire. A classmate came in and placed an emergency call, which I heard, saying her car was on fire. I walked over to an extinguisher, grabbed it, popped her hood, discharged the extinguisher under the hood, and the fire was out. The fire dept. arrived a few minutes later, I spoke to them and told them the car was still hot, and the fire was out. And I went back inside to study. Some of my fellow students were "amazed" that I knew what to do and acted. To me it was and for most people it should be nothing to really get excited about. I think the posters here with fire training would think this was small potatos, as far as a fire goes. But for some of my fellow students, these highly educated and intelligent people would not know to grab a fire extinguisher, read the instructions and use it. Their minds were not trained to deal with any situations that required such actions.
Part of the learning and knowing what to do needs to include testing yourself to know that you will be able to think and act correctly when TSHTF or in any time of need. IMO, the way to learn how to handle some stress is to sometimes put yourself under it. I think Blast's mention of Hacksaw and Taurus using and testing out their gear is part of this.