So pg's years of experience getting better than random results is irrelevant and you'll only believe him if he does a long experiment (that would cost him lots of money if it's not just luck) to prove something he already believes?
It's unclear whether he's getting better than random results. You're assuming the consequent.
It's well-known that the most successful startup in a group of startups is likely to earn more in profit than all the rest combined. We're here on HN talking about PG because YC has been the most successful of all incubators. However, there's always going to be one incubator that significantly outperforms all the others as a result of the distribution of startup success.
I don't know enough about how well PG's investments have done to make informed judgments, but only a very select few people are likely to have that info. I suspect those people have also done their due diligence to figure out if YC is a value-add compared to other incubators (it should be possible to do this without a convoluted double blind experiment), but anyone who's not them really can't say for sure that that's the case.
This is oversimplified. In many cases, it is the conjunction of a reasonably strong prior belief and the absence of preexisting "proof" that motivates a scientist (or mathematician) to try to prove something in the first place.
The key is to perform proper Bayesian updates in the face of evidence in either direction; if you do, as long as your prior wasn't totally insane it doesn't really matter where you started.
Launching a successful startup is luck BUT selecting entrepreneurs/startups who have luck is no random. You can definitively find some metrics to evaluate the current luck of a startup and expect that the founder has enough skill to continue to maximize luck in the future.
