When your existing investors don't maintain their pro rata in a new financing, prospective investors will wonder why. This assumes that the existing investors: (1) Have already invested in your company (duh), (2) Have some knowledge of the company (e.g. served on the board), (3) Make it a habit to invest in follow-on financings like yours.
You can still get around this if you have a good excuse, e.g. "Our existing investors are out of money". And your existing investors confirm your excuse when prospective investors inevitably call them.
So if USV didn't participate in the latest Twitter round, the company and USV probably had a good excuse, e.g. "Our fund isn't structured to make acceptable returns at $1B valuations". When a random angel who isn't on your board doesn't invest your Series A, most prospective investors won't wonder why.
Regarding YC-Sequoia:
The firms who are likely to invest in post-YC companies are likely to be mavericks who can think for themselves. That's the kind of investor you want anyway. You don't want to tell prospective investors that Sequoia spent three weeks intensely studying your company and decided to pass. But the fact that Sequoia could have looked closely at your company, but didn't, will probably be irrelevant.
On the other hand, if Sequoia and other YC insiders are cherry-picking the best YC investments before they hit the mass market, good investors are going to get less interested in demo days. That will hurt YC companies.
I don't know how these forces and other forces will play out in the marketplace. And since we're talking about game theory, the existence of this thread will influence the outcomes.