Why would Valerie Jarrett go to South Africa? Can’t he go anywhere without her?
She's his handler. Just like royal children needed minders whenever they went in public, to keep them from picking their noses or doing something unseemly, so VJ has to keep an eye on the self-indulgent child occupying the office of the President. She really blew it with selfie-gate, and I think this photo shows her over-compensating for the error.
Jarrett gives the order to Obama.
Obama approves.
Jarrett then makes it happen.
And Obama has deniability.