Does relativistic mass curve space-time, i.e., does relativistic mass affect the gravitational field of an object?
So we can not say, what would have really happened, we can only say, what would an observer observe. Do correct me if I have missed something...
If two observers watching the same event, saw different outcomes to the same experiment, that would be a problem. Usually different observers will see events happening on different time scales, but they must see the same outcome or else there would a contradiction.
For instance, the Lorentz transformation 'explains' why different inertial observers always see the same outcome to an EM experiment.