I don't know where you find your "Definition" of OPCON, but according to DOD Dictionary
OPCON Defined as
Command authority that may be exercised by commanders at any echelon at or below the level of combatant command. Operational control is inherent in combatant command (command authority) and may be delegated within the command. When forces are transferred between combatant commands, the command relationship the gaining commander will exercise (and the losing commander will relinquish) over these forces must be specified by the Secretary of Defense. Operational control is the authority to perform those functions of command over subordinate forces involving
organizing and employing commands and forces, assigning tasks, designating objectives, and giving authoritative direction necessary to accomplish the mission.
Operational control includes authoritative direction over all aspects of military operations and joint training necessary to accomplish missions assigned to the command. Operational control should be exercised through the commanders of subordinate organizations. Normally this authority is exercised through subordinate joint force commanders and Service and/or functional component commanders.
Operational control normally provides full authority to organize commands and forces and to employ those forces as the commander in operational control considers necessary to accomplish assigned missions; it does not, in and of itself, include authoritative direction for logistics or matters of administration, discipline, internal organization, or unit training. Also called OPCON. See also combatant command; combatant command (command authority); tactical control.
http://www.dtic.mil/doctrine/new_pubs/dictionary.pdf
Do noted that OPCON is a command, NOT A FULL COMMAND as I mentioned in my previous post. OPCON command aspect only in Organisational Level. As it pointed out in the explanation above. The way you use it, however, denoted a full command of a unit.
Each Command have its own works, the problem is, you can be under organisational strength, but without logistic, without training and doctrine, without tactical control over a unit, CFC cannot command actual troop on the ground. Yes, they can put all of ROK military under the CFC as that is organisational command, but then since CFC does not offer any of the logistic, TRD and tactical control. The "Command" is in name only.
it's like the relationship between 101st Airborne Division and XVIII Airborne Corp. The 101st was represented at OPCON level at XVIII ABC, however, the Tactical and Theatre Level command for 101st is still under regional HQ of 101st. The reason being, 101 is no longer an Airborne Division, they (XVIII Airborne Corp) would have no actual control of 101 beside the HQ attachment. The DOD doing this for the lineage of 101st Airborne Division. Not because of the actual level of Command and Control.
As I said, only the forces of attached to KATUSA and JSA are under US and UN command respectively.