I apologize, this should be a comment to unknown's posting of "THEOREMS FOR A PRICE", but I lack sufficient reputation.

Doesn't a proof that says "Goldbach is over 99.999% likely to be correct" have to be 100% correct? In other words, doesn't even a post-rigorous proof have to be rigorous somewhere?

I think this is precisely what Terry Tao is getting at with his comment to the original question. In fact, I'll go further: it feels like some people who are questioning the need for rigor want to jump immediately to Tao's "post-rigorous" thinking without having gone through the "pre-rigorous" and "rigorous" phases. This may work for some prodigies, but I doubt it's a good method in general. But then, I believe in rigor!