Quote: Should this apply to people who fall off mountains or people who start fires by smoking in bed or leaving chip pans on? Should they be left to look after themselves?
Two different situations there.
The lone mountaineeer is somewhat akin to the lone sailor, he is risking nobody's life except his own [unless he falls on someone!] and if he gets in a jam he can only hope that a mountain rescue team will help him, in the same way that he would be willing to help other mountaineers.
Someone who starts a fire in the way you suggest is not only risking his own life but is also putting his neighbours at risk. It is in everyone's interest to deal with the fire and, in any case, he does pay for the Fire Brigade so even though he may be a bloody fool, he is entitled to their service!