In any situation involving a gun, firing it at a person should be taken as intent to kill.
No reasonable person would fire a gun into a door with somebody else on the other side in the expectation of not killing them.
Well, 'should be taken as' is an inference. Normally it holds, but as you say, this is true of reasonable people. My neighbour killed a burglar and was done for manslaughter, on the grounds of diminished responsibility.
The higher court used the formulation, 'he should have known it could kill, therefore he must have known, therefore he did know', and this is what the judge had objected to.
In parts of the US, I wonder if P would have got off completely, on the grounds of castle doctrine - you can shoot an intruder. I don't know.