Often, "arbitration" is used as window-dressing for a severe power imbalance to continue. Arbitration only deserves to be called such if it's entered into voluntarily by two parties with good intentions.

How could GitHub initiate anything better than a third-party investigation? Is there some way to turn yourself in for an alleged crime, then deny that you committed the crime and go through the government court system? It's not clear to me what GitHub could have done better.

Arbitration is not about justice, it is about the appearance of justice, while being incredibly stacked against one party. Arbitrators are paid by the party that demands arbitration (the corporation eg. cable, wireless, etc). If the arbitrator does not side with the party that is paying their fees, they get called on to arbitrate less and less, until they are no longer employed as an arbitrator. That is a perverse disincentive to ever find against the party paying your fees. It is much cheaper than going to court, and and you win 90% of the time. What's not to love?

I'm not saying anything one way or another about what GitHub did or didn't do. It's my general observation that "arbitration" is often other than what it says on the tin. This comes from personal experience, and I think it's a valuable general observation. I hope that you are not coming at this from some kind of "you're either for us or against us" standpoint.