The WGA rules require 1/3 original material to obtain credit on a film. However, if the director is one of the writers it bumps up to 1/2. Any WGA member is also entitled to arbitration, but in a case like this where the director is not a WGA member I don't really know how it would work. That's all of course assuming that the production company is a guild signatory, but as they had other union crew members they probably are.
My guess is that both directors were advised not to push for credit, or that if they were it was determined that neither rose to the required 1/2 level of material contribution.