We receive the notice, lock the repo, and inform its owner why it's been locked. At that point, they can either remove the infringing code or make a counter claim and we'll unlock it provided the original party doesn't file a court order.
More info: http://help.github.com/dmca/
After that it would take a court order to get it taken down again, but that would mean the repository owner will be liable for the damages, not github.
This is the one part of the DMCA that actually seems to work reasonably well. If you're confident that your stuff does not infringe then it's back up within a very short time and you know you're on the hook for any further fall out.
(IANAL)
As someone who runs a site that hosts content, this is great for us. We aren't allowed any sort of leeway in interpreting the claims and in return we are exposed to no liability. We are simply the middle man and have to do what's asked of us.
Fighting your legal battles is not a feature of Github. At least not of any of the advertised service levels.
I imagine they have to lock / disable all forks beyond what the notice mentions as well, unless Sony, et al don't understand how git/github works.
Just consider Youtube a moment. Couldn't they minimally run a hash on any uploaded/embedded sound and see if it matches the hash of some taken-down material before? It'd probably catch at least a significant number of users even if it's trivial to bypass and susceptible to compression losses and quiet-extensions and so forth. (An AI could always "listen" to it though and probably perform pretty well.) Anyway, Youtube doesn't make an automated effort to take down infringing material (that I know of) so I don't see why Github has to.
You don't have to do any forensics in the sense of your youtube example, you just have to follow the graph.
Whether that it is a legally compelling point, I have no idea.