You are legally correct that GitHub in isn't obligated to take down a work if they receive a DMCA notice. But that would be very bad advice to take. GitHub handles millions of repos. GitHub could take a huge gamble by keeping the material posted after a DMCA request, or just take it down, wait for the DMCA counterclaim, and put it up after the counterclaim was filed. A CEO could easily get fired for risking the entire company when there was a no-risk alternative with the same result. The legal penalties are so stiff, and so easily avoided, that it would be improbable for a company to do anything else. This apparently isn't a DMCA takedown anyway, but I thought I should comment on your response.
Anyway, I'll repeat myself yet again: They need a lawyer.