GovCloud claims that it's used to "manage sensitive data and controlled unclassified information (CUI)."

I don't think the US government is dumping classified info onto corporate cloud environments judging by this description from GovCloud. But there's plenty of info that's sensitive but unclassified and the government does need to function in a lot of ways that doesn't involve state secrets.

https://aws.amazon.com/govcloud-us/ for more of a description of what GovCloud actually is.