Fight Fire with Fire?

I thought the saying was You can't fight fire with fire, but they can and do. It's been a common practice since the old west, when they burned underbrush so there wouldn't be much flammable debris to prolong a fire. And more recently, when they detenate dynamite to remove oxygen from the fire, which extinguishes it. Shakespear mentions "be fire with fire" in a play about King John, written in the 16th Century.

The closest reference was more recent.  US author Henry Tappan's 1852 reminiscence A Step from the New World to the Old, and Back Again:

Smoking was universal among the men; generally cigars, not fine Havanas, but made of Dutch tobacco, and to me not very agreeable. I had some Havanas with me, and so I lighted one to make an atmosphere for myself: as the trappers on the prairies fight fire with fire, so I fought tobacco with tobacco.

But it still makes more sense to me that you can't fight fire with fire. I think it is more effective to fight fire with its opposite, water. There are many instances of the backfire thing, back firing, meaning althoughit was intended to quell the fire, it only exacerbated it!