Not necessarily -- you can have the really big decisions made by consensus in a horizontal fashion while still delegating much of the decision-making power. No one's arguing that everyone in the organization sit down for every decision. There's no need for everyone in the organization to sit down and decide whether candidate X is a good hire (though that might work just fine for really small teams). Delegate as much authority as possible to the actual experts in the domain and the stakeholders of that decision. As decisions affect more and more people, figure out ways to involve everyone in that decision making process in a horizontal rather than a vertical way. Asking "Who's responsible making sure the code is high quality and we're not taking on too much technical debt? or "Who's responsible for making sure we're in legal compliance?" or "How are you going to resolve a disagreement about which vendor to use for XYZ" is a different question entirely than "Who's in charge of everything?"
I have no idea of YC internal procedures. I will comment a bit on the concept of flat organizations.
IMO, it's much more efficient if each individual focuses on his domain and provides a single interface for the stakeholders for that facet of the enterprise.
The overhead of communication and context synchronization become ginormous as the organization grows and the issues affecting the enterprise grow in number if every decision is made on a flat basis. If the context synchronization is not made then the decisions made by the group will be less informed than that of an individual. For informed decisions, it would require then that each individual become an expert on the single issue discussed. This would effectively negate the main benefit of small teams - individual focus and small communications overhead.
A flat organization cannot rapidly scale. And sometimes there might not even be a consensus. Having an overriding vote, albeit rarely, is crucial to break deadlocks.
This is not to say that flat organisations are bad. But I don't think they are a particularly good fit for the scale YC companies work at.
"Who's CEO" is good shorthand for "do you know who's responsible for what kind of decisions?"