It should take much more legal effort and 'application of mind' to effect disruption.
I want to make it clear that I'm not arguing for the legal grounds here. I'm not a lawyer, so I will leave that to them. I'm arguing from a more moral/ethical stance.
I'd like to disagree with you. By allowing you to run under their umbrella, I feel that Github has a responsibility to take care of you, and the data that you put on their site. I feel that it is quite insincere for them to say "Sure, put your code on our site!" but then kick you to the curb as soon as there's any trouble. There's definitely a level of extremity that I don't expect from them: I think that after a certain amount of legal argument, they should pass it to the uploader, but I feel like their default attitude should be "no, you can't just attack the uploader because you feel like it."
It sends a clear message to the FOSS community that they don't care about taking care of their own, which is bad for Github, and bad for the committers.
I'd be curious though: Why do you think that "The law requires them to forward them to the account publishing the content without any consideration of the merits"? It's my understanding that they do have some grounds here as it is their site.
EDIT: I reworded my post as the original was rude, and accusatory.
This. This is the main topic here. The wide use of centralized services (such as Github, but it applies also to Facebook, Google et al.) makes you dependent to corporate decisions, including coward (or maybe rational) decisions towards freedom of their users.
This is also why linux kernel developers will never, ever use a service like Github. Apart from scalability issues, the single point of failure that these services are (not for technical reasons, but for political reasons) is simply scary.
TL;DR: Assholes who send buggy DMCA is not the issue here. Depending on a centralized service is.