Mr Clutterbuck (love the name) is correct, the map does not take into account soil
I can't speak much for the east coast, but as for the west, yes Perth is pretty much exactly the same climate as LA. The only difference is all of Perth is pure sand down the centre of the earth.
LA has infinitely better golf courses, largely for economic reasons, but imagine how much better again they would be if they had Perth's soil advantages. Pure, free running beach sand and much greater flexibility in construction and then huge amounts of ground water to hold the grass over the the hot dry summers.