Should I have stopped the car? What's the legality of the situation?

You are responsible for the operation of your vehicle. If you need to deal with any braking emergency, unsecured items; and yourself; are going to continue at the vehicles original speed. You know how this works since you've witnessed it. As a driver; you have a greater responsibility for avoiding contact with pedestrians. If you hit one; you can reduce their multi-million award by claiming there were a couple of thousand dollars worth of contributory negligence. You have no troubles with the jogger since there was no contact. Your obviously upset; as anyone would be. You have learned a hard contact lesson about hard braking. Maybe practice a few lock ups in an empty parking lot. This way it won't come as a surprise if you have stand on your brakes again.