"You will find this hard to believe, but I'll report it to you firsthand: some companies turn down the opportunity to get funded."
Not all that hard: my last employer turned down VC financing. And I'm going a similar route with my own startup: I'm not averse to VC financing, but only after achieving "product/market fit". There's no sense taking other people's money for an idea that may not fly, and I can change direction more easily without employees or investors.
I still would like to see actual numbers for the 4 quantities I mentioned. My point is not that you're wrong, it's that without that data, you can't draw a sound conclusion either way.
"What percentage of them get good deals, and what percentage get tranched, 3x prefs, tiny valuation, and loss of the board?"
One of the advantages of YC, as I see it, is that this is far less likely to happen. YC brings bargaining power: if a VC screws over a YC startup, you can bet that YC will not be bringing any future deal-flow to that VC. You don't have this advantage as a lone startup, regardless of how good your product is. Never underestimate the power of incentives in getting people to behave properly.