Can the union be reported to EEOC for failure to represent?

Question

A white employee strikes a black employee on the job. The black employee is punished. The union refuses to represent the black employee. Can EEOC get involved?

Answer 1

Not the EEOC. You want the National Labor Relations Board.

Answer 2

That sounds terrible but I have heard similar things before. Unions and other organizations are often corrupted by nepotism, racism and greed. Is it possible the agressor is related in some way to someone in authority within the union? It happens that many unions make jobs available to their own relatives and friends before passing jobs along to line workers. Once hired, those relatives/friends have a cozy relationship with union officials and management.  

Let's face it union officials and management officials know how to skirt the rules.