The YC application isn't a legal document and Kyle (having gone through YC) knows this. Legally he'd have full ownership and in the application specify 50/50 me

The YC application isn't a legal document and Kyle (having gone through YC) knows this. Legally he'd have full ownership and in the application specify 50/50 meaning if/when they formalize the relationship that is what the equity split will be. YC doesn't really care what the actual current/legal split is at the time you write the application. What they care about is what the split will be by the time you start YC because that is what is relevant to them. And (my guess) is that the real reason they care about the split is that they're looking for red flags. i.e. is the cap table already messy with lots of people on it? Is the split NOT 50/50 signalling the founders don't consider each other equals which is a bad sign, etc.