This is why YC's audience is typically college students and very recent grads, who are less likely to have additional obligations. Or, rather, originally the YC concept was geared towards this audience, and the funding amount is an artifact of that.
I think they will cover whatever you want initially (eg, moving expenses, renting a place), but my interpretation is that that comes out of the 5+5n.
If I was doing YC for a summer, I wouldn't need to move. I could just fly there with a couple of suitcases and a laptop, but I'd need some way to cover my existing apartment rent. That's a pretty significant expense over 3 months. And I suspect YC is not looking for companies who see the experience just "doing YC for a summer."
1. Move
It's easier to do it in three steps:
1. "Do YC for a summer" 2. Secure more funding 3. Move