The President has the authority under the AUMF to commit our forces to combat operations. If the President decides he wants to commit forces to Iran, he will stipulate how many he wants to commit. The Secretary of Defense then has the authority and responsibility under the law to deploy forces according to those committments.
It’s the president that orders the troops to be deployed, he decided how many would go and told Gates to make it happen.
Your whole premise seems to be that somehow Gates has more authority and responsibility than Obama does for the sole purpose of removing Obama from Lakin’s chain of command.
As anyone that has ever served will tell you at any command in the Armed Forces the chain of command is always on display from the president on down to the unit commander. Trying to pretend otherwise is a fool’s gambit.