I think you ought to win this bet.  There is nothing in the 501(c)(3) rules that prohibits payment of compensation to directors of charitable organizations.  Nor am I aware of any state law that prohibits reasonable compensation for services actually rendered.

Compensation is frequently paid to directors of private foundations but rarely paid to directors of public charities.  The Standards for Excellence promulgated by Maryland Nonprofits and other state associations throughout the country require that charity board members serve as volunteers, although that is not legally required. In either case, the organization must be sure that the compensation is reasonable or there could be taxes on self-dealing for private foundations or excess benefits for public charities.

Many public charities include a provision in their bylaws prohibiting compensation for directors.  If your friend was thinking of a specific organization that has such a provision, he might be able to argue that the result of your bet is a tie.  But if your question was more generic, as it sounds, it looks like you win the whole amount.