Michael, first off, I don’t have superior knowledge or such. I’m often wrong. I don’t mind being proven wrong as it is a great learning experience.
In the attached picture you will see the amperage charging rate for an alternator. Notice that at low RPM’s of around 1000 to 1500 RPM there is minimal output from the alternator. The alternator doesn’t start kicking in strongly until around 2000 to 3000 RPM. Keeping in mind Ohms law of Watts = Volts x Amps. So if you have lights, seat heaters, rear defroster, fog lights, defogger, and more on, then you probably have a need of about 700 watts. Now 700 watts divided by 12 volts = 58 amps. As you see from the graph, to get 58 amps from your alternator you need to be around 3000 RPM. Well, what happens when you are just sitting there idling at 800 RPM and only putting out 8 or 10 amps? You start draining the battery! This is why on a cold morning when you go out to start the car, turn on all the accessories and then go back into the house for 15 or 20 minutes to finish breakfast and then come out to a vehicle that has stopped running with a dead battery.
As to your example of running a vehicle and pulling off the battery terminal, yes, as we now know your alternator will put out about 8 or 10 amps at idle. That is more than enough to run the electronic ignition, ECU, fuel injectors, and other small circuits that require the running of the vehicle. If Chrysler would have turned on the headlights or such in their demonstration, the car would have died quickly. If you can’t tell, I use to teach automotive at the local college.