They have it right, the Sec Def is the conduit to the forces and he works for the President. The joint chiefs of staff are like military advisors to the president. They give advice and military capabilities (options). There is no formal chain of command between the other two branches to the military. Think of it like a local city government. The Police Dept has a Police Chief, he works for the Mayor. The city council (congress on the city level) has no authority over the police department except budgets. The City Court has no authority over the Police force only the Mayor who is the top City Law Enforcement Official.