I’m not an attorney, but I don’t see the connection to ATP either; I hope a real lawyer will comment. I suspect ATP (which probably has its own corporate counsel team) will move for summary dismissal.
That said, in this case, I see the issue more as this instructor’s actions as PIC, rather than an issue of instructional liability (which would have been the case if the student crashed while acting as PIC without the instructor aboard).
As for due diligence, the Pilot Records Improvement Act requires that “air carriers and operators operating under 14 CFR parts 121, 135, 125, 91k, and air tour operators (91.147)” hiring a pilot check into that pilot’s record, but there is no such requirement for hiring flight instructors. For more on the PRIA, see this FAA web page. That leaves it to the jury to decide, absent an explicit requirement for due diligence, what level of diligence was incumbent on the flight school involved.