The book in question is British Sea Power: How Britain Became Sovereign of the Seas by David Howarth. A section claims that before modern painkillers and aneasthetic, people were more inured to pain. How true is this claim?
Like almost any claim of this nature it is almost impossible for people today to know variables like pain tolerance at that time which would require scientific knowledge which was not possible at the time. Likewise it is also almost impossible now to determine pain tolerance at this time in history in any empirical way.
If the original quote is that people were more "inured" to pain, I'm not sure the author is suggesting that they had higher pain thresholds. I think perhaps he's saying they expected pain in a way we don't.
Modern medicine is very good at pain control and modern patients have come to expect that surgical procedures are accompanied by anesthetic and analgesics.
Consider a simple tooth extraction. Today your dentist numbs your gum and jaw before he starts pulling, 150 years ago you'd maybe drink some whiskey and prepare for agony. It's not that the historic person has a higher tolerance for pain, it's just that he knows there's no option.
unless he has specifically referenced his claim there is not really any evidence for it. As ArchiveMonster said, it would be almost impossible to asstertain pain tolerence in the past.
You must remember if someone has taken a large wooden splinter to the leg, for instance, they'd have a massive amount of adrenaline being released into their body, so when the surgeon removes the leg it might not feel as painful. The sailor would also be suffering badly from shock so might not quite understand what was going on.
I had a little look on the link you provided, he doesn't seem to have referenced anything which is annoying