Contradicted by evidence, some years ago.
A study in a dental clinic used measurement of local-anaesthetic to measure how pain-sensitive redheads are..
It took .. was it 10% more? Definitely more, pain-killer for the redheads.
The genetic-defect which codes for red-hair, and splotchy-skin, also codes for being more pain-sensitive.
It also explains why redheads are "more reactive" as lifelong-pain-sensitized people naturally would be, doesn't it?
( I look Irish: my hair's gone white, but the fur on my arms is still orange )