The issue of continuing to fly is nothing to do with Virgin. It was a medical decision. The fact that Virgin paid the doctor's salary is irrelevant. Whether the doctor was correct in continuing to issue a medical would require an expert opinion based on his notes. So we cant decide, only postulate. Medical negligence would be very difficult yo get past a court because the standard against which the doctor would be compared would be a generalist occupational health doctor or a GP, not a consultant psychiatrist. In any case the pilot made money by continuing to fly, he didnt lose money, so there is no financial loss.
The pilot had a medical so Virgin was not at risk
Virgin may have failed to take out loss of license insurance in which case in the UK it would merely be a breech of contract and a matter for an employment tribunal or the county court for financial loss.