To me it seems like the employee was "asked" on at least two separate occasions to remove the jacket. it further seems, to me, that round one and round two are connected. Round 1 failed and round 2 tried again. Round one refused to leave until the employee removed his jacket. Probably the same for round 2, and that would explain why the veteran was escorted off of the premises.
If you read the caption on the image it says "me and a few others". At least three, probably four military personale are in the store and they want this employee to remove his jacket. Sounds like a bit of intimidation, whether they realize it or not.
If this illegal, what happened to calling the police? Are military members super citizens in which their demands supersede domestic law and order. Of course not. They Absolutely do not have the right nor the authority to demand that anyone do anything, especially within the context of an old navy store.
It feels like these guys are stalking this kid.
That is exactly how I would take it. If this is not in violation of the Valor act and it is legal for the kid to wear it ( particularly if he bought it , and is NOT trying to impersonate a Military service person), to me that is the end of the discussion. If these military people do not like it, then don't return to Old Navy.

Most of us will still continue to patronize Old Navy.
I wish they still had the Antique Truck in some of the Stores