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Have you considered how many electric watts are involved? One HP is equal to 745.7 watts. 1000 HP means 745700 is supposedly being utilized. Taking into consideration the IR losses and heat generated and that no electric motor or system runs at 100% efficiency, then more than 745700 watts is actually required to attain a mechanical 1000HP. Sounds like a bunch of hype to me.
There are a few ways to look at this,

Are you disputing the motors are 250 kW ea? I am attaching a photo taken at GM's drive unit test facility, clearly these motors have been run on the dyno, so GM knows the output capability.

Or do you dispute that the battery can discharge at that rate? So the Hummer EV has a 200 kWh battery, so discharging at 750 kW, would be a 3.75c discharge rate which is fully within reason for short bursts.

for reference Tesla Model Y Performance outputs 336 kW from a 75 kWh battery for a 4.5c discharge rate. So as you can see the Model Y makes the case that there is no issue with the discharge rate.

Another interesting thing I saw in the Hummer demonstration is engaging the WTF mode, seems to take some amount of time, are they charging a capacitor for a power boost during this time? Possible, and would lessen the strain on the battery.

I do not think GM is going to BS about the output as they know customers are going to take these right down to their neighborhood chassis dyno, and likely break the dyno..

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