Yeah, the government doesn't really have servers. They outsource that to government contractors. By "Government Servers" what one really means is FedRAMP compliant cloud hosting facilities owned by IBM, CGI, Dell, HP, and other tech giants and protected by access privileges that rival some maximum security prisons.
Are they at risk? Sure. So is every computer hooked up to the Internet. But anything hosted on "government server" is probably 10 times safer than a server anywhere else.