About the relation between output current (to a fault) and input mechanical power: e.g. does 300% current mean 300% torque.


It's perfectly reasonable that a synchronous generator can produce several times its load current to a fault, without needing more than the rated mechanical input.  That's because a synchronous machine - unless in a really unusual design - has a high reactance compared to its resistance. If the fault current drawn from the generator is mainly reactive, the power can be low in spite of the high current. If you want to think in terms of torques, you could say that the reactive component of current is in the wrong position (compared to the machine's field) to contribute to torque.


At the level of big generators this is one of the classic issues for power-system stability: if a generator is loaded hard, and then there's a short-circuit on the line that connects to it, then far from loading its prime mover more, the generator in fact starts to run away (accelerate) because it's producing less active power than when there wasn't a fault. It's rather counterintuitive if one thinks in terms of batteries and dc machines. At transmission level, reactance is a lot more than resistance.


Back to the present case: if the fault is at the end of a long circuit with plenty of resistance, then the situation could potentially change so that the generator actually does supply more power than its rating. I'm not sure of typical parameters for these standby generators, but generally synchronous machines tend to have remarkably high reactances: e.g. Xs=100% which would mean dropping the full-load voltage across the synchronous reactance when at the full load current. Although also sounding strange, it can work because the drop adds at 90degrees to the load voltage for an active-power load, and the AVR has pushes the excitation up by e.g. 50% to handle the load. With such high reactance it would be hard for any fault to extract a much more than the rated power (if the AVR doesn't go beyond what's needed for full load), at least for more than a few cycles. At shorter times, as that manufacturer brochure mentioned, the behaviour after a sudden change is governed by a lower apparent reactance than 'Xs', which is because currents are briefly induced in rotor windings when the stator current changes.


[Edit:  I got distracted while writing, and missed later posts .. more has emerged about the generator in question, so I could have avoided mention of AVRs. Still, the point is relevant about faults not necessarily causing big mechanical load.]