And where does the payload land on the 1-in-100 launches that the orbital insertion motor fails?
Pretty much the same place as the payload on a current launch if its insertion motor fails. Were you under the impression rocket-based launches don't use insertion motors?
Not quite. Current launch technology (read: rockets) are powered through much of the atmospheric flight. MECO occurs outside the atmosphere, and the craft's flight path takes it over uninhabited areas for the thousand KM until it is outside the atmosphere. Therefore, at no point is the vehicle on a trajectory such that if it looses power, it will intersect the Earth in an inhabited area. The balistic tragectory of the 'Slingatron', however, does bisect the Earth at roughly (due to atmospheric drag) the same place where it was launched from. Also, one needs to take into account the possibility that the payload will leave the muzzle at lower than expected velocity. Thus, an entire great circle of the Earth, several tens or hundreds of kilometers wide, potentially falls within the craft range.
The insertion motor isn't necessarily a single-purpose item; for example, the Shuttle used the same motors for insertion that it used for the rest of its on-orbit maneuvers...but one way or another, you either insert or you come back down.
Yes, I am aware of the functions of the OMS. And I believe that there was an abort mode for failure of the OMS, though it was not an OTA.