You know, there's a long held view that when someone says something like "I didn't believe in ghosts, but then I saw one and now I'm a believer", they are being a bit disingenuous.
The fact the book is called "proof of heaven" leads me to believe he is very much religious, and took little convincing.
If someone genuinely doesn't believe in something, they don't tend to change their entire belief system based on a single tenuous instance/experience. Especially a neurosurgeon. The logical first step would be "oh, I had a really weird near death experience. As a neurosurgeon, I'm going to look into the neurological signals sent as you die and see if there is something that causes these weird hallucinations". They don't immediately go "I SAW GOD!!!!".
I don't believe in ghosts. If I saw "something", I wouldn't say I saw a ghost, by the very nature I don't believe in them. It would take multiple people witnessing the same thing with me, where there is no other possible explanation, for me to consider changing my view.
Edit: some info from wiki.
The book was a commercial success but also was the subject of scientific critique in relation to neurology, such as medically induced coma and brain death.[1][10][11] A 2013 article in Esquire magazine refuted claims made in the book.[1][10] The doctor who treated Alexander stated that certain details might not be true, such as claims Alexander made about speaking clearly at times he would have been intubated.[1] The Esquire article also reported that Alexander had been terminated or suspended from multiple hospital positions, and had been the subject of several malpractice lawsuits and that he settled five malpractice suits in Virginia within a period of ten years.[1][12]
Among the discrepancies, was that Alexander had written the cause of his coma was bacterial meningitis, despite his doctor telling the reporter that he had been conscious and hallucinating before being placed in a medically induced coma.[1][13] In a statement responding to the criticism, Alexander maintained that his representation of the experience was truthful and that he believed in the message contained in his book. He also claimed that the Esquire article "cherry-picked" information about his past to discredit his accounts of the event.[13]
Proof of Heaven was also criticized by scientists, including Sam Harris, who described Alexander's NDE account on his blog as "alarmingly unscientific", and that claims of experiencing visions while his cerebral cortex was shut down demonstrated a failure to acknowledge existing brain science with little evidence prove otherwise.[14] Neurologist and writer Oliver Sacks agreed with Harris, and argued that Alexander had failed to recognize that the experience could have been the result of his cortex returning to full function at the outset of his coma, rather than a supernatural experience.[15] In 2012 Alexander responded to critics in a second Newsweek article,[16] where he said that he vividly remembers having periods of hallucination and explains that there was a massive difference between them and his 'fully immersive' visions of the afterlife. Alexander describes the hallucinations in his book, saying that they were disjointed and centred around both random events and his doctors. He then compares them to the "hyper-real" experience of the afterlife, and says they do not match up. He also made a prediction in his book that secular critics, which included himself before his coma, would attempt to discredit him and his experience without looking into it properly.