The Boston comment may get the most press, but I think the most important thing he said is the next 5-10 years comment, that it will be about what we build now that connections are mapped and, importantly, available to tap into. It's not a secret and not the first time he's said that, but to me it reinforces that FB will keep doing app-friendly things like Open Graph.
For better or worse, the issues discussed in the article also explain why programs like YC are becoming more and more of a necessity. They are one way a VC can cut through some noise, and one way a good entrepreneur can stand out from the crowd.
Google doesn't necessarily squeeze out all competitors in any industry they enter, but they do raise awareness. In some sense this is great for Dropbox because I would guess well under 50% of computer users even know cloud storage services like this exist...but many more will if Google enters the market.
The problem, of course, is if they all learn about it through gmail and Google captures them all, but I think that underestimates Dropbox's ability to counter.
Lastly, don't discount human laziness aiding Dropbox customer retention - time is a switching cost here.
I know of trading firms who will sue to try to enforce a mostly unenforceable non-compete agreement on a trader who leaves just to piss them off and waste their time and money to protect themselves (and try to scare others from leaving in the future). But...this is the exception. No one said hedge funds were rational!
While YC may want to be the default choice for the best ideas, they also love and support the startup scene. Given they can only accept a fixed number of companies each class, they're cheering this. More startup support worldwide makes that many more bored cubicle-dwelling programmers worldwide think that much harder about leaving to pursue their dream, which benefits YC.