Well, as he says in that book, the disease was acting upon that bundle of the physical body and "I" consciousness, so he didn't suffer at all because he wasn't identified with the body or the "I" consciousess. Along the same lines, it's not you that's reborn unless you are identifying with time-bound, impermanent elements.
But I think you need to go a bit deeper with it. If you think you are the one who's been pulled into existence, then you must be sure who you are. So, back to the basics, I think Ramana and Nisargadatta might recommend that you find out who it is that you believe is being subject to birth, death and rebirth.
I think it's important not to get too caught up in ideas and views because, apparently, they're basically dreams anyway. So, going with the basic atma vichara, and shikantaza, just see how thing actually exist and function right now. Don't take other people's word that this happens and this happens. It's all hearsay until you really experience it yourself.
Well, like I said, I don't think non-duality is exclusive from duality. Don't get too caught up in worldviews.
I've also been afraid of it. Being attached to my loved ones is the biggest thing keeping me from not being attached to the world. My loved ones are the only reason im attached to the world. But, no one goes anywhere if we are to believe Ramana and Nisargadatta. The differences and seperation are superficial. I don't think there's actually anything to lose, even though it really seems like there is.