Classifying their actions as arrogance is an interesting take on the event. It does rather overlook the fact that they might have been expressing concern for the sailor's ultimate safety. The Navy has just as much right to utilize international waters as the next person. If one feels that their rights of passage are being interfered with by such exercises they can, of course, feel free to ignore naval warnings in international waters. Personally, as a master of merchant ships, my policy was to avoid all naval activity at all times. Naval flotillas are prone to erratic actions and do some dangerous things while burning up the taxpayers money. Some of those things happen at high rates of speed, often in excess of thirty knots, so the ship you didn't see could well be running you under in less than a half hour.
Arguing with the Navy on the high seas is the equivalent to arguing with a state trooper alongside the road at two in the morning. We all know how it's supposed to turn out, but the question is, do we really want to press our luck and find out?