The original quote was fine. The headline lied about the quote.
Well, the original quote was rather out of context. They were using it as a sort of gotcha and once the full text is seen it puts it all in a new light.
I could say “Hitler thought jews should be exterminated”
Headline “Sharrukin says: ‘jews should be exterminated”.
The quote is factually true, but out of context, and therefore false. You can lie by telling only part of the truth.
I agree with your point about the post headline being a fabrication.