There's e.g. https://aws.amazon.com/govcloud-us/details/ these days. Azure and Google have government offerings as well. Safe to say neither would be bothering if the government didn't use cloud products these days.

http://fortune.com/2016/09/02/us-government-embraces-cloud/

Looks like even the CIA is using some AWS.

"U.S. government agencies are moving to cloud computing and away from their own data centers faster than private corporations"