Your "trick" shows whether or not the other person will consider the whole range of things you could have meant instead of assuming the most likely thing in their judgement. So it's useful. It reminds me of shit tests in dating where you trigger situations just to see their reactions to certain situations.
Regarding why you can't just say the same thing word for word, that's because shared context matters.
This is basic social skills. If you don't have the same shared background and context, then it's unclear if you mean one thing or the other.
So when one woman says "Think about what a white man would do", to another woman, there's the implication that they're talking about their shared experiences regarding society's expectations around women.
When a man says that to a woman, especially it's a white man saying that to a black woman, your contexts and backgrounds are so wildly different that surface area of what you could mean is quite large.
So when you had the chance to clarify yourself and you backpedaled, that made it look even worse because it implied that you had bad intentions and were trying to take your words back.
So yes, it's true. You can't say the same thing word for word as one person say to another if you and the other person do not share the same contexts.
Regarding why you can't just say the same thing word for word, that's because shared context matters.
This is basic social skills. If you don't have the same shared background and context, then it's unclear if you mean one thing or the other.
So when one woman says "Think about what a white man would do", to another woman, there's the implication that they're talking about their shared experiences regarding society's expectations around women.
When a man says that to a woman, especially it's a white man saying that to a black woman, your contexts and backgrounds are so wildly different that surface area of what you could mean is quite large.
So when you had the chance to clarify yourself and you backpedaled, that made it look even worse because it implied that you had bad intentions and were trying to take your words back.
So yes, it's true. You can't say the same thing word for word as one person say to another if you and the other person do not share the same contexts.