Constitution:
Article II, Section 2, paragraph 2
[The President] shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments.
Technically, the Senate could vote on all appointments, in practice, the Senate votes on all major Presidential appointments:
http://www.senate.gov/artandhistory/history/common/briefing/Nominations.htm#8
That out of context excerpt is not about the military