I'm very skeptical of that claim. It seems just as reasonable that he has a perfectly normal brain that is exactly as afraid of things as the rest of ours, but he's spent a lot of time doing terrifying things and has learned to suppress how his body reacts to it.
you can find his brain scans and see that his visual to amygdala connecting path is activated significantly less than for normal people (which in other words is "much less afraid of danger"). It is a question though whether it is a result of training or an original anatomy.
He doesn't behave the same, where normal climbers would freak out and do a fatal mistake he repeatedly remains calm as on sunday tea party. You can train some resistance to fear of death and indeed all climbers do (myself included), but almost everybody hits some wall within their current skills. His wall is way further than almost any other climber. Not that he is the only soloist, far from it.
The only abnormal thing about his brain scan was that his amygdala activated less than usual when he looked at frightening or disturbing images, which would be entirely compatible with deliberate desensitization (perhaps through ~20 years of practicing climbing with no protection?)