Rather, it's that there's a deep interdependency between the three variables of language, programmer, and problem that give rise to a system like HN+YC (which was a single program until 2014). If you changed any one of those variables you'd either have gotten something radically different or nothing at all. So my statement is a bit like saying that YC would not exist without PG; and your objection is a bit like saying: that's an exaggeration, any person who did the same steps at the same time could have arrived at the same place (and perhaps better since that person might have been a better manager as well).
(Not only PG built YC, of course! But PG wrote the software and that was a critical piece.)
I'm not saying that all programs have this property about programming languages—rather, that some do, and they tend to be particularly interesting and creative. For another example, one might say that Unix would not exist without C.
There would be more interesting and creative systems in the world if we were more open as a community to these unexplored spaces. We exclude them in order to have the feeling that we know what we're doing, and we reinforce this by ridiculing and dismissing deviants. The social dynamics that exclude new creative possibilities are incredibly strong, which is one reason why when systems like this do end up succeeding, they tend to be the work of loners, weirdos, or people who have some strange mutation to withstand social pressure. (This by the way is the origin of the "$weird-language is only good for solo programmers" meme, ironically confusing cause and effect.) No doubt other fields work the same way; software is just the one I know well enough for the mechanisms to be obvious to me.
An analogy just occurred to me, which I want to note so I don't forget it. The relationship between a program and the language it's written in is like the relationship between a piece of music and the instrument it was composed for. To say "this system could have been built in some other language" is like saying "this music could have been composed for some other instrument". That may technically be true; music gets transcribed for other instruments all the time, just as programs get ported to other languages. But it misses the most important thing: the creative process by which the music or program got written in the first place.
There are intimate feedback loops between the mind of the composer, the developing music, and the design of the instrument—which possibilities it makes natural/easy vs. which it discourages/excludes. Every instrument and every programming language has a different set of these. They may not differ in what can theoretically be played on them, but they differ immensely in how they organize the space of possibilities—which ones are near at hand vs. out of reach. You can play the same scales on the piano, the cello, and the guitar, but where the mind goes next as it composes a new sequence of notes—not a scale, but a sequence that has never existed before—is deeply conditioned by the instrument it's working with, which is the medium it's growing in. Some next-notes are far more likely than others, and which next-notes those are differs greatly between instruments. In the same way, a program grows by accruing constructs (expressions, statements, forms, types), and the ones that are most likely to get added next are the ones that are most natural and nearest-to-mind, given the program so far. Which next-constructs those are differs greatly between languages.
Since each next-note or next-construct is deeply conditioned by the sequence it's adding to, this effect compounds as the system grows. It follows that, at least for the most interesting and creative systems, a program is literally unthinkable apart from the language it grows in. So much for "languages don't matter"—yet how often that untrue truism is repeated! The reason for this fallacy is that we take a program as if it existed prior to being written, which is impossible.
So when I say HN/YC would not exist without Arc (or Lisp really), I mean it in the sense that https://www.youtube.com/watch?v=rGgG-0lOJjk#t=14 would not exist without the cello even though https://www.youtube.com/watch?v=mhfxM5FOzjQ#t=3 is a thing, https://www.youtube.com/watch?v=x6GZ6xeGnJQ#t=15m would not exist without the piano even though https://www.youtube.com/watch?v=XXGCfW-cGoE#t=91 is a thing, and https://www.youtube.com/watch?v=skdE0KAFCEA would not exist without the electric guitar even though https://www.youtube.com/watch?v=kNFpOh2seqo is a thing.