This is a bit of a naive explanation.
Let me explain how a DDoS mitigation strategy works for many of the companies listed in the summary. They setup datacenters in 10, 15, or more places all hosting a proxy. Some of these solutions use DNS to route traffic around problems (GSLB) while others like CloudFlare use Anycast which is awesome and super hard to get right. Each of these services are typically setup with tons of bandwidth capacity, well over 10Gb, but often times into the 100Gb range. They also often have deals with upstream providers that can filter traffic at the edges meaning it never makes it onto the internet in the first place.
Since you servers are not exposed to the internet, and the ones are are have far, far more horsepower to deal with this than a DDoS will even manage from the client side they can easily just churn through the attack, discarding connections and never letting them hit your limited servers. This is how they can easily survive Anonymous style DDoS attacks.
The other thing is to ensure you have turned of every "feature" your load balancer is giving you. SSL termination at the LB, full session management, etc. All of these cost load balancer CPU which is easy to take advantage of, even if there is a DDoS mitigation system in front of your site. You can't just add a few more servers either. Adding capacity to a load balancer is nearly impossible to do mid-attack.
Even more interesting is that you can often times trick the crappy ddos software by doing things like excessively slow responses (tarpitting) making its loop take ages to try again. This is pretty much using the tactics of a DDoS directly against the attackers.
Another common tactic is to add attackers to a view in your bind config that resolves your hostname to 127.0.0.1 just for them. This works if you do not have long TTLs and they are using hostnames. If they are using direct IPs then you simply move your traffic to a second IP and drop the one they are attacking. Best case is if you can do this via BGP announcements so the traffic simply will fail to route and everybody wins.
And yes, I do this professionally but not for any commercial product.