I hope you're kidding. GitHub has no legal basis for transferring ownership, and it would be a publicity fiasco if they did. A "reasonable case to ownership" at best would allow to bring the case to court.
"Account names may not be inactively held for future use. (...) Inactive accounts may be renamed or removed by GitHub staff at their discretion."
Sounds fairly benign. Ownership transfers happen all across the web with, to give a few examples, subreddits, social media handles, messaging groups, etc. Why can't Github do the same?
Edit: GH could also be in for liability claims should the original owner re-appear (at least in general, if not this particular case), and would need to check identity of the involved parties and whatnot, which is going to be very costly.
Nobody is giving away the current org - github would just be vacating the old name so somebody else can have it.
This is bound to become a bigger issue in the future as more and more names get used then fall into disuse.
The lesson is again why it it so important for any organization or project to have a continuity plan and not to have any one person as a gatekeeper.