Probably a silly question, but how do you know they're not active on Twitter? I mean, outside of well known elected officials here (like the US president, UK prime minister, mayors, etc) I'm not sure there's much of a reason for people to state they work for the government on social media sites.

Might be a fair few government employees who just don't tie their social media presence to their real identity for one reason or another. If I get a role in the UK civil service I'm certainly not putting a job description in my Twitter profile, but that doesn't mean I work for MI5.