There were no 'secret' army units. You might be assigned to a unit that was using a unit name (Studies and observation group, for instance) that had a publically stated headquarters location and goal but was at undisclosed locations doing classified work.
I was once the post adjutant for a local American Legion post. I used to get inquiries from applicants who were in 'secret units' who had no public records or who were doing such secret work that they did not "exist", or from the wannabes whose records were destroyed in the St.Louis records center fire. One of our members was an 0-6 serving in J1 at the Pentagon about ten miles away.
He shared with us, a copy of an army document detailing 'secret units' and the records lost in the infamous records center fire. Everyone in the U.S. Army is assigned to a unit of public record listed in the army TO. The so called records fire in St.Louis only destroyed those records of U.S.A.F. personnel who were decharged in the late 50s or thereabouts.
In my long association with veterans, I have encountered WWII veterans with faulty memories, Korean Veterans who were trying to forget and about 10,000 Viet Nam veterans who were just out and out lying about their service. If you encounter a Viet vet who tells you that he was a clerk or cook or truck driver, he is surely telling the truth. If someone claims to be a 'grunt', he is likely telling you the truth. But if you encounter someone who was an 'airborne ranger, sniper, green beret or CIA assassin, do not leave your change on the bar when you go to the bathroom. To be sure, there were several dozen trained army snipers, hundreds of brave souls serving in division LRRP units that were later flagged as the 75th Ranger Regiment and thousands of gallant men who served in the 5th and 1st special forces in VN. Only problem is that I have met about ten million of them in the ensuing years.