You are correct. Pilot simulator training often presents RTOs as engine-related events while the Takeoff Safety Training Aid (1993!) gives recommendations about other failure conditions to consider. The majority of all RTO accidents were not related to engine problems. In these cases it is possible that the pilots were not fully prepared to recognise cues of other anomalies during takeoff. Pilots often interpret these other anomalies (like a tire burst) as events that threaten the safety of flight and decide to reject the takeoff at any speed. Indeed it is not easy to put these other than engine failure anomalies in the simulator.