I read both the book and this review, and while the review makes some valid points, it also holds the book to a pretty high bar.
Usually I'm all for doing exactly that, but this book is not about hard scientific proof for some fancy new theory. It's about an idea, the idea that humans are good by default. To be taken seriously as an idea, it only needs as much proof as the idea it's rejecting, which is that humans are a razor thin layer of civility over evil, savage animals.
It's about debunking that as much as it is about proposing an alternative. I think Bregman is perfectly happy to leave the hard science for the scientists. If readers agree that his idea is at least as plausible as the one he's up against, he's done pretty well. And to my reading, even this review agrees with that.