Interesting incident, fortunately without any injuries. I must wonder if where the problem lies; with the crew or with the system? In Europe and elsewhere a landing clearance is only given when the preceding aircraft has vacated the runway and the runway is ready to accept the next landing aircraft. The policy of giving the landing clearance concurrently to multiple aircraft clearly invites this kind of incident, be it due to stepped on transmissions, radio failure, or, as in this case operator error. Implementing a safer system seems sensible!