Old ladies with no training whatsoever have been known to defend themselves successfully with handguns.
And children with no training whatsoever have been known to drive vehicles sucessfully while old ladies with lots of training have been known to be totally incapable of driving safely.
Nevertheless, in terms of controls, I agree with you, the average handgun is simpler to operate than the average car.
But actually making a gun go bang is actually the simplest part of using a gun. It's the legal, safety, social , etc, aspects, of firearm use that make it similar in complexity (perhaps even more complex) to using a motor vehicle. I just don't see how you can give the legal aspects of deadly force a proper showing in a 30 minute session, and I don't think it's realistic to assume (for example) that a person with a handgun, a 30 minute familiarization session and no range time is going to be effective and safe in a house with no power in the middle of the night.
Regardless of that, the analogy is very good for one simple reason.
An incompetent person can purchase a car and get a license (no driving test required in my state). An incompetent person can purchase a gun and keep it in their home (no license required in my state.)
But, those two actions place absolutely no responsibility on you (or me).
Lending someone a gun when you know they don't know how to use it, or lending someone a vehicle when you know they don't know how to use it is irresponsible. Even if you try to assuage your conscience by giving them a cursory training session.
And, both of the hypothetical questions skirt the important issue--if these people in question had taken responsibility for their own safety/transportation, all this would be a non-issue. This is the REAL issue which is carefully camoflauged by making an emotional appeal. I.e.: "Your FAMILY member or FRIEND needs HELP NOW!"
How does the saying go?
"Poor planning on your part does not constitute an emergency on my part."
I'm not really that cold. I would try to help them. I might offer them a place to stay for the night. I might offer to go stay with them for the night. I might offer to give them some REAL firearm training (like mossyrock described) and/or help selecting a firearm.
I just don't consider interjecting a handgun into a situation with an untrained, stressed out person to be a true help.