Private Fire Station Companies in NYC?

Many people may not know it, but the subways in NYC were privately built and run for many decades until city price controls drove the firms into bankruptcy. Here is something that I noticed at the end of a story about fire stations in NYC.

The firehouse was built in 1906. It was the former home of a unit of the Fire Patrol, a private firefighting organization backed by the insurance industry.

I wonder how much of the fire services in NYC used to be privately run.