I think what General Ward was trying to say was that we do not use private security companies to protect US missions in Africa. Local guards (Africans) protect US embassies and consulates in Africa just like other local nationals protect 260 US missions in all other locations except Iraq, Afghanistan, and one or two other high threat areas.
USG does employ contractors to deliver training and other security assistance.
Who has primacy? Rather - who has resources? And authorities. SecDef has
argued for two years or more that State needs resources to carry out its mission. DoD budget is around $650-700 billion; State is $25 billion to operate 265 overseas missions plus $25 billion in foreign assistance. Much of the assistance is earmarked for foreign military financing, contributions to international organizations and humanitarian projects. Very little goes to bilateral or regional security assistance in Africa.
Isenberg mentions a few of the programs. None of them are large. All of them are difficult with high political risk. Even combined, they are small ball compared to DoD programs.
Then there's the fact that USG couldn't get an appropriate African country to host AFRICOM. These countries may want some mil-mil, but they don't want a US COCOM and they certainly don't want our military training their civilians or gendarmerie. That is one reason why CJTF-HOA is such great proof of concept. USCG programs in Kenya and the Gulf of Guinea too.
State using contractors is a fig leaf that covers a full range of jerry-rigged solutions.