I read that book a few years ago, and at first I was taken in by it. But before I'd even finished reading it I became skeptical and started reading online about how his claims are likely false. For one, the claims he made about the weather at the time are wrong. But also, there is the issue around how his career was in jeopardy at the time, so maybe he wrote the book to dig himself out of that hole? But also, like you said, he has no proof that it all happened while his brain was inactive.
It's just one person's story, so how can we know it's true? It irritates me when I come across people who hold this book up as irrefutable evidence of near death experiences and therefore an afterlife. They're like: Look! He's a doctor and he got a book published! It must be true!