Working on GovCloud requires ITAR which is citizen or "permanent resident" (green card). There are other positions that require a security clearance, but GovCloud does not. GovCloud is open to non-governmental customers who need to meet stricter requirements (it's not solely for government use).
It's still pretty apt, the reason the non-government customers are in GovCloud is almost always because their customers are in the government. For example, if you want to sell a service to US government departments, you'll find it much easier to do so if you have a presence in GovCloud yourself.
