And plenty of GM alternators failed trying it. And you underestimate the power required by a refrigerator. A 16cu ft frost free refrigerator draws an average 724 watts. That's a LOT more than 3 amps.
The statement was people can "run their house" on a 1000 watt inverter run off the car battery. 60 watts for a tv (or more) plus a few 60 watt room lights - you have 300 watts in no time, then the fridge comes on. Or you attempt to run your furnace. (another 500 to 800 watts). The 1000 watt inverter is going to be running pretty close to it's limit - and so is the 100 amp alternator.
If you want short term, extremely limited power at very low efficiency, run your car engine at idle to charge your 12 volt battery to run your inverter. Much farther ahead to just buy a cheap 1000 or
2000 watt generator and siphon the gas out of your car to run it. The generator can be purchaced for less money than a decent 1000 watt inverter.