I can guarantee you that there have been times where the top military brass walked into a meeting with the president with 3 options and left with an order to come up with something better. I have no insider knowledge but at the end of the day the president has the final say. Now I don't know how frequently the president overrides his military advisers but it must happen.
Not only that, but it's not like the head of state is alone with the military brass in such meetings. There will be people there both from the permanent civilian bureaucracy as well as advisors of some type from the party in power.
Ultimately, military grand strategy is a domain of politics as much as it is about how to wage war. The agendas and objectives are ultimately continuations of political goals of whoever is in power. During a war, the fighting must be coordinated with diplomacy, economy/trade/manufacturing and public relations/propaganda, all of which generals tend to know little about.
And even if the President is not the one making the micro decisions, he/she definitely is responsible for making sure the war is waged in a way that is aligned with the general objectives of the administration.
This means defining objectives, access to resources as well as defining the rules of engagement. And equally importantly, listen to the military and determine when the time is right to actually provide additional resources or permissions, despite political costs.
