Sorry GitHub, that's not for you to determine, as you are not a US judge. They should never have replied like this IMO and this behavior opens them up to liability for not properly handling DMCA procedures.
Proper DMCA 512(h) notices (assuming OP's was proper) require the host (github) to remove or disable the content first without even attempting to verify the claims.
Then the repo owner has a chance to challenge the notice. If they choose to do, they're basically required to publicly doxx themselves first, by nature of just going through the motions of the judicial court system.
If there was no challenge after a set period of time, then the content stays down.
If there was a challenge, it stays down until a court decides what happens next.