I personally know of two cases in older homes where it was the paper backing on
ancient insulation up inside the wall that caught fire. That situation can be
very difficult to deal with. In both cases, the homeowner had quick access to a
garden hose, but was unable to do anything other than slow the spread a little
while waiting for the F.D.

This is generally because people trying to put out fires in their house
aren't usually willing to wreck the wall in the process, and that's what's needed.