Why emotions cannot be assigned numbers?

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Upon continued re-reading I keep coming to the conclusion this paper is asserting patient reports are reliable because they verified it with brain scans!

It does not say brain scans are unreliable. Brain scans are what they used to verify the reliability of patient reports.

The part you quoted in bold warns about generalizing over kinds of pain, while remaining confident about pain magnitude.

The title of the paper is, "Neural correlates of interindividual differences in the subjective experience of pain." They found those titular neural correlates. With brain scans. They got different brain scans for people reporting different levels of pain in response to the same stimulus. Certain brain areas were much more active in the individuals reporting more intense pain in response to the same stimulus.

If we're not in agreement about this basic point, that they confirmed the reliability of patient reports with brain scans, and by no other means, then there's no point in branching off into the other topics you introduced.
 
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Pythagorean said:
also, let's not forget that this report was for pain, which is much easier to characterize (both subjectively and objectively) than emotions.
But the OP is about emotions, not pain.

So we need to get back on topic please.