Hmm. I don't know the answer, but here is my noodling.
Consider a separately excited synchronous generator feeding a unity power factor load at its full capability, with no other sources of power in the system. What sets the short circuit current of that system?
The short circuit current is set not by the full load rating of the generator, but by its impedance. If the short circuit current were the full load rating, then the thing would be some sort of constant current source, like a bicycle alternator.
At the instant of short circuit, I think you could consider the induction machine to be acting like a synchronous generator where the excitation has just been shorted and the magnetic field is starting to decay.
I think, that in general, the short circuit current contribution of an induction motor will be different from either the locked rotor current or the full load current.
-Jon