I should also mention that setting up two legally separate -- but totally intertwined -- organizations in this way is something that almost all large advocacy organizations do - from the ACLU to the NRA and many/most other Wash DC groups.
In the public's mind, the two orgs are indistinguishable (which is totally understandable).
Of course, I may be wrong -- the NAACP may only be one org, they may have violated laws, etc in this case but I would be very surprised if that were the case. This stuff is pretty much "non-profit 101" for board members, senior staff, the org's general counsel, etc.
Actually, the NRA is NOT a 501(C)3 organization. It plays fair, and not a dime given to it can be deducted. The NRA makes no false pretenses as to what it is and what its aims are. As for most of its left-wing rivals, they play dirty pool and get away with it. If any of them were even questioned, the liberal press would have a field day over the abuse of power in a purely political way by the IRS.