The scale of attack that is required to completely bring down any of the large services that we use on a daily basis are so large that they could otherwise be focused on the DNS infrastructure, or the internet infrastructure of a decent-sized country. Much smaller attacks have been used in the past to take out large IRC networks (hence disrupting communications for hundreds of thousands of users). Mail bombs, spam attacks on news groups, internet worms, etc etc. This has all been going on for years. If anything, companies like Facebook and Google are better equipped to deal with the threat than most, because they have the resources to do so as a high profile target (note that I don't include Twitter in this category, because they have had trouble staying up under normal loads).
So I don't think this highlights the fragility of "the new internet", it's just the fragility of the internet in general. An attack on the scale required to take down Facebook would be able to cause similar amounts of disruption almost anywhere it was targeted.
If anything, I think the rise of rapid provision of cloud computing resources are probably making the internet _less_ fragile, in that a well-designed application can scale proportionally to its (legitimate) user base within hours or days, not weeks or months as it used to be.