Put that way, it doesn't quite sound right, either. But it's true. My nephew is a veteran with a medical discharge. He receives a small monthly check, but does not have PX privileges.
His dad left after 15 years. Again, no PX privileges.
To be able use the commissary/PX/NEX et cetera, one must be active duty, retired after 20 years, or 100% permanent and totally disabled...