GitHub apparently follows this process exactly--without any deviation. GitHub does zero investigation to determine who is in the right--even in a case as obvious as this. Mr-Steal-Your-Script's user name alone should be enough to let GitHub know who owns the code. During this entire process, GitHub communicated with me entirely by computer-generated responses. I never had an opportunity to explain the situation to an actual human being. So, if I wish to pursue this matter further, it seems that I have no choice but to hire a lawyer.

So GitHub follows the legal process set out for hosting services? Umm, yeah. No shit. They're doing exactly what they're supposed to.

I do not even have the option of suing Mr-Steal-Your-Script to pay my lawyer's fees, because he is anonymous. As blatant as his theft was, I have to assume that he has covered his tracks well enough to remain anonymous.

GitHub should have provided you with his counter-notice including contact information. If they've accepted a clearly invalid counter-notice then you can sue them.

Otherwise, yeah, this guy has posted a copy of your code, and the only way to take it down is to sue him. That's how copyright infringement usually works - it'd be the same if he were hosting it in ISP-provided webspace, or his own personal site, or printed it out on a physical billboard he owns. I don't know why you see this as being about "the Corporate Internet" at all.