While the fantasy fan in me can certainly appreciate and even enjoy the points listed above, the skeptic within me raises a hand. "He" has some rebuttals to each point.
1: There have been many documented instances of people experiencing physiological death and yet returning to a living condition. Many such people have accounts of Near Death Experiences, some bordering on the ludicrous and others seeming more realistic- all having a sincerely spiritual tone. While Enoch Root might have experienced a technical death, it is not impossible that he somehow rallied against the odds and pulled through. Stranger shit has happened in real life.
2: I have seen many people move with such speed in critical situations that it would appear, from certain perspectives, that they were moving in a "wraith-like" manner, like the wind itself- Enoch's dark, priestly robes would certainly lend credence to the notion of him appearing like a shadow beneath the canopy of a deeply forested area while he is moving quickly on foot. One such as Enoch Root, who was undoubtedly trained in various forms of martial arts throughout his many years as a spy (among other things), would be entirely capable of moving with great alacrity. I have seen Tai Chi masters who are pushing 70 years of age move faster than I could track them with my eyes. And the bit about Enoch Root quietly whispering something in a long-dead language... he was, after all, a priest and he had just killed a man. Perhaps he was giving his victim Last Rites, postumously, in the long-dead language known as Latin. To continue, my personal take on that particular event in the book led me to believe that Enoch had actually shot a land mine close to or beneath his intended target, which had caused a very large cloud of debris and smoke to plume upward and, in a way, cloak Enoch's movements. One moment he is standing in the river, holding his gun, he sees the knife-wielding Andrew, says "Fuck it," runs towards Andrew with his gun drawn, fires at the ground beneath Andrew's feet and detonates a mine in the process, which blows up right under Andrew, and when the smoke clears he is standing on the river bank. Finis.
3: America (Amy) Shaftoe, who had been severely injured in a hostile incident was admittedly out of sorts, psychologically. Whatever Mr. Root might have done may have occurred so quickly for her that she was not able to disseminate, exactly, what he did or how he did it. Also, she was the daughter of a Marine veteran, who took personal battle very seriously and often chose to keep a tight lip about such experiences (a soldier's mentality of "leave the battle ON the battlefield" extends into his private life, more often than not) and may have taught his daughter a similar philosophy. She also may have been reluctant to talk about the incident because, to her, it was intensely personal and her upbringing probably enforced itself, instructing her to, in a sense, cherish her close brush with death in as private a manner as possible. Many war veterans choose not to talk about their experiences, even with those they love dearly, simply because they want to leave those memories in the past. That day was, after all, pretty rough for all parties involved. And Mr. Root's on-the-spot remedy might very well have been something he learned from the natives- the jungle is a very big place indeed and quite dangerous. Various nasties lurk about in those deep forests and the natives have probably learned quite a good bit about how to perform seemingly miraculous medical techniques in crucial ways that "modern medicine" can't even begin to understand. Do a Google search on "voodoo" and "puffer fish" for a decent idea of what was discovered by third-world natives and is now of great interest to the global medical community. That which is at first not understood might appear to be very much like magic, but is in fact just a unique application of natural resources.
4: It does not surprise me at all that Lawrence Waterhouse considered Enoch Root to be a "wizard." Root was, in terms of a spy, a "Jack of all trades," a man whose talents were not limited to a single area of expertise. His resources, through his organization, bore some similarity to the Illuminati, an organization which has been around for literally centuries and seems "tapped in" to nearly everything around the world. For someone who might have been initiated in the organization at an early age (as certainly seemed the case, from Enoch's own account of his personal history- he was an orphan who had been adopted by his organization), Enoch Root's familiarity with certain, mysterious facts about that which is not commonly known does not seem surprising to me at all. To someone who is not familiar with Eruditorium, Enoch Root might very well seem the 1940's equivalent to a wizard- or even a master spy whose security clearance is so high that they merely call him a "wizard."