1. It's not ethical to use a story that you know is false just because you know that it will work -- whether your goal is to get a spirited discussion of an issue going, or to persuade others to change their perceptions of that issue, or both.
2. That doesn't mean you can't use the story. It just means that you have to word it in such a way that it will be easily recognized as a parable, or as some analogous hypothetical form, rather than as a factual report.
And you suggested a variety of different ways to put that second point into effect.
So suppose we start with that infamous story of The Wicked Welfare Queen, which almost everyone has agreed would be unethical to use in the form that Ronald Reagan presented it...
"You know what really gets to me? Makes my blood boil? I work like a dog, just trying to keep a roof over my family's head and food on our table, and I pay every last damn penny of my taxes! And what does the government do with my money? Hey... let me tell you what they do with it! They give it to a Welfare Queen that drives around in a fancy pink Cadillac, and wears a mink coat, and has $150,000.00 in her bank account.... You know what's in my bank account? Maybe enough to pay my phone bill, if I'm lucky! And you know why that is? It's because most of my money, what I make working my tail off every single day, goes to the damn Welfare Queens!"
... and we revise it to make it clear that it's not intended to be factual; like this, for example:
Revised Generic Version
"You know what really gets to me? Makes my blood boil? Hearing people tell that crazy story about a Welfare Queen that drives around in a fancy pink Cadillac and wears a mink coat and has $150,000.00 in her bank account, when they know perfectly well that there's no such person and never has been any such person!"
I think that would be just as effective as a way of getting a discussion going and would introduce the same conversation points, without introducing the ethical problems.
[I have not forgotten, however, that many of you would prefer a more elegant English register than the one I use; feel free to post alternative revisions that you'd be more comfortable with.]