> the sentence talks about imaginary pain

It does. But read what the sentence says about "imaginary pain"—that it still hurts. That feeling of hurt is pain. So the sentence is saying that "imaginary pain" is just "pain". So pain that you might think is imaginary, is actually real.

Or, equally, pain that you might think is real is actually imaginary. (If the two terms are equivalent, substitution should work in either direction.) Seems obviously false to me.

> No, the sentence talks about imaginary pain, not real pain with imaginary causes.

That's exactly what you're getting wrong. "Imaginary pain" does not mean "imagining a situation where imaginary-you is in pain". It means pain with imaginary causes that applies to the real you.

That's not a possible meaning of "imaginary pain" in my dialect of English.

Seems like the sentence might just be a poor translation from Swedish.

But pain is subjective by definition. What does "imaginary pain" mean? The answer can only include some notion of "cause."

Imaginary pain is pain in your imagination, just like an imaginary car is a car in your imagination. If you stub your toe, you are really in pain and not just imagining it. If you imagine stubbing your toe, you are only in imaginary pain (assuming that you imagine it to be painful).

Precisely. You brought up cause (stubbing your toe). You're agreeing with me.