>"why did Rails Machine throw out the site so quickly?" If you run a datacenter, you pay for an uplink. That uplink has limited capacity. 4gbit, 10gbit...whatever. A big attack can saturate that link completely, so even with the biggest most expensive "mitigation device" on the market (some of this gear can get into the hundreds-of-thousands-of-dollars for /one/ device, mind you), if a DDoS is overloading your upstream bandwidth providers, you can either have your entire DC brought to a crawl, or null route the site.
With that said, how did CloudFlare keep lulzsec up? Anycast, lots of iron, lots of smart technicians, and probably tens to hundreds of thousands of dollars in bandwidth fees. TL;DR it was a publicity stunt that they very smartly played up.
DDoS is pretty misunderstood, and lots of clients think that there is some magical box that can take all the traffic. Again, if your link is saturated, a "mitigation" device can only filter the traffic; your upstream providers can and will take you offline if you don't fix it. Failing that, you get a massive overage bill and every other client at the facility is crawling. It's not really a good solution (mitigation devices /can/ help with smaller attacks, but for the big stuff, null routing is the best solution unless you have something like CloudFlare -- and even they will pull the plug if the attack gets too heavy, because it's simply not worth the expense to them to keep your site online.)