This was an interesting point which I missed at the time. However this situation would only occur extremely rarely in the normal running where the timestep is set small enough to produce reasonably accurate/continuous behaviour. Basically a state is so intricate and detailed that a coincidence of that kind is difficult to envisage, among multiple bodies, holding space and velocity values. And since going forwards or backwards in time always produces a single solution, (rather than multiple solutions) the idea of multiple plausible inputs still seems reliant on rounding error to me or numerical oddities which get more unlikely the more precision and smaller timestep is employed.