Sorry, not an expert and I have never been an entrepreneur so forgive me if I am misunderstanding, but doesn't YC give them money? In order for this statement to be true either (1) having startup seed money has no bearing on success or (2) YC gives the same money to people it rejects as to people it accepts.

Unless being a part of YC adds value which I suspect it does. Impossible to really test this unless YC would provide the same level of support and resources to other companies.

Depends on what "luck" entails. Success is measured by something--for the sake of argument, let's sake acquisition price. But there have to be proximal factors; to be a bit reductive, no one is arguing that large companies pick randomly for the world of startups and them for millions of dollars. Perhaps the most immediate proximal factor is number of users or revenue or...whatever. You wouldn't say, "if it was just luck, companies would preform just as well whether they had users or not".

So the question with luck is how far down the causal ladder you start considering things inputs (i.e. things which may or may not influence the outcome) instead of outputs (i.e. things which might be the result of those inputs or of luck). So with YC, is that getting or not getting into YC is an input variable that we could check against success, or is getting a YC spot one of those proximal factors, and the luck was just in getting that, at least in part?

So the "is it pure luck?" question isn't very well defined, but the GP's argument might still be useful in answering it. Moreover--larger questions of luck aside--it would be helpful in determining whether the YC selection process is actually useful. But probably only if they didn't tell anyone about it.