Savor that, “As head of the Pentagon, Hagel would not determine foreign policy.” No, he would not. But he would have substantial control over the information, advice, and policy options available to the person who does determine foreign policy.
Suppose a president were to request an assessment of a hypothetical strike on Iran. Suppose the secretary of defense delivers to him a plan requiring the insertion of US ground forces into Iranian cities to be sure of destroying relevant facilities. That “plan” is as much a veto of a strike as any decision.
Donald Rumsfeld enabled the Iraq war by producing estimates it could be won with as few as 135,000 troops. Had he instead on 300,000, the war would not have occurred: it would have seemed too heavy a lift. (As indeed it proved.)