That said, I stand by my basic analysis and conclusions: this was a very sick man whose behavior was an involuntary consequence of medical derangements, and who was abandoned to die.
This discussion is focused on claims that the captain was negligent in two respects. (1) negligence in failing to properly address the man's medical issues; (2) negligence in not retrieving the man after he went overboard.
You make a strong argument with regard to the first issue, but the captain won't be judged by a jury of medical doctors. He'll be judged by a jury of ordinary people who have themselves had to struggle with difficult decisions about when to call the doctor for a family member with a fever or kidney stones or vague chest pains. Those ordinary citizens can be expected to set a high standard for the line where criminal liability begins, because they will understand that one shouldn't be branded a criminal for a mere misjudgment. For this reason, I think the outcome of this case will be of great interest to every skipper who sails offshore and has a crew member become seasick.
Moreover, the account that is contained in the original news article contains this information: "David Pontious appeared to be experienced. A story published in October 2015 in the Beaufort Gazette said he attended seamanship school in Florida, taught sailing lessons out of San Francisco and was a U.S. Merchant Marine officer for a time. He was also a member of the Beaufort Yacht and Sailing Club, officiated races and had a day job in health care technology
." He was a highly experienced sailor who was well aware that it would be a long trip with no access to health care. More than anyone else, he should have been aware of his own physical condition and he should not have boarded the boat. Did the captain discuss it with him? Did he assure the captain that "it's nothing," and that he "had some pills that will take care of it"?. Did his assurances cause the captain to defer to the man's own assessment? Were his periods of hallucination of brief duration with long periods of lucidity in between, during which he continued assuring the captain that he'd be ok?
Perhaps the truth is as simple and straightforward as you suggest, but I suspect the captain has an account that hasn't been heard yet. I suspect that, at trial, the defense will portray the man as the author of his own demise and portray the captain as a decent fellow who trusted the man's assurances too much.
With regard to the second issue, when the man attacked the captain and choked him, that constituted lethal force, and the captain had a right to use lethal force to defend himself. If he had a firearm, he could have shot the man to death to stop the lethal attack. The fact that the man was sick or deranged doesn't detract from the captain's right to defend his own life. As it happened, the captain didn't have to use lethal force. The man jumped overboard. If the prosecution suggests to the jurors that the captain should be subjected to criminal conviction and punishment for failing to pull the man from the water, I think it's entirely likely that the jurors will conclude that the captain had no obligation to bring the man back on board and give him a second chance to kill the captain and crew.
There are strongly held opinions by sailnetters on both sides of the issues, and I think it's likely that there will be a similar spread of opinions among members of the jury. This will not be a slam dunk case on either assertion of negligence' and a hung jury wouldn't be a surprise.
I think the captain's least defensible action is in his failure to promptly report the incident.