OK. I think we need to clear a few things up

1. issuing authority is congress
2. Hillary may have given medals to some troops but she did not issue them
3. the VA has nothing to do with medals -they can not issue or replace them
4. Your discharge papers show what happened while you were in the service.

If Congress says you are entitled to wear a ribbon, no CO can stop you form wearing it.

Here is the question, can you wear a medal or ribbon which you have earned but which is not on your discharge papers. the answer YES - as long as you have indeed meet the requirements for the award.

As and example if you look at marine unit awards online they give a time frame and award and say anybody with the unit during this time frame
the NAVMC states
(1) All personnel permanently assigned or attached to thecited unit who were actually present and participated in the action or actions for which the unit was cited are authorized to wear the ribbon.

There is not further stipulation that they must be handed the award or that it has to be written on the dd-214 or other discharge papers

The other question is are you authorized?

Public Law 107-314 legislated the creation of a new medal to recognize military service in the Republic of Korea and the surrounding waters.
Members of the armed forces authorized the KDSM must have served in support of the defense of the Republic of Korea. The area of eligibility encompasses all land area of the Republic of Korea, and the contiguous water out to 12 nautical miles, and all air spaces above the land and water areas.
The KDSM period of eligibility is July 28, 1954, to a future date to be determined by the secretary of defense.
If you meet the qualification set by congress you are authorized.. No further authorization is required.. getting it added to your discharge papers may be good but it is not neccassary