The car behaved exactly as it should (ie. avoided hitting idiot, unshielded meatsack regardless of priority) , the cyclist should have ridden on.
Four way stops aren't common in the UK (I've never seen one), but are in other countries (South Africa, Australia). The rules are pretty simple: first come, first serve. Arrive at the same time, yield to the right/left as per usual. In the event 2 cars opposite arrive and one is turning across the other, the turner enters the junction and waits for the other car to go straight across. The turner then has priority over all other cars outside the junction. It's really simple, also way easier and fairer than all the idiotic roundabouts we have in the UK.