Not only greencard holders but ITAR even has exemptions for non-US persons, that is those who aren't US citizens or Permanent Residents.

I don't work directly with anyone like this but I know SpaceX has a few, not sure of the exact number, employees who are neither citizens nor permanent residents.

From what I've heard the process of getting a non-US person ITAR cleared is extremely costly, both in time and money and is thus used very sparingly.