As others have stated, the company / government owns the computer, not you. And, as such, they also have IT policies (often written in employee guidelines, or even as a big fat warning message when logging in) that all activity is monitored / logged and can be dug through if and when they please.
There is a sort of unwritten "acceptance" at most jobs that employees will use their computers for outside activities. EG: an employee paying some bills on the computer during their lunch break, or surfing the web for something for their kid or what-not. As folks go up the executive / management ladder, they're often stuck in their offices 12 hr days, and it's just a given they're going to use their work computer for personal activities.
In a perfect world, people would keep their personal activities only on a device they themselves own. But, it's not a perfect world.
In good IT settings I've been in, the IT folks (all IT / IS folks, really) act as guardians of secrets. The IT folks are monitoring everything that goes on on every computer in the company / workplace / college campus (for college computer labs) / etc .. but unless they have REASON to look into something, they just ignore and overlook any extracurricular activities. (EG: at my last job, I would IM with my gf all the time. The IM's would get a bit saucy, but nobody was dragging me off to HR dept to talk to me about them. I was a good employee that did my work. Could they have? Sure. But, at most companies it's a "we don't care unless we're asked to look into something". Managers were surfing the web in their offices. They were checking their bank accounts. None of that information was used against them, because our IS / IT dept had a policy of protecting it's employees and their personal information. And, an employees activity on a bank site has nothing to do with the company.. unless, say, the employee is embezzeling money from the company into their personal bank account.)
The only times I've seen IT investigating things is when some law was broken or a complain was filed. EG: someone's been embezzeling money.. obviously the IT dept is going to dig through that person's emails and computer with a fine-toothed comb to investigate. Or, an employee complains about someone watching porn on their computer (you'd be surprised how many execs sitting in their offices think they're completely isolated and private, but someone walking by sees something saucy going on on their computer.. and a complaint is filed with HR. Then the IT dept has to go to work and look at logs.. and eventually have a talk with the exec to tell them to stop visiting whatever site they're visiting.)
So, this makes me think they had reason to look into what you were doing. Maybe those two people are jerks and go out of their way to find things on their employees in order to hold them hostage or throw them under the bus. If that's the case, I'd find a new place to go work. (Hard enough just to do a job, worse still when you have a boss actively trying to work against you or get dirt on you to hold you hostage over something.)
There are petty managers that think "managing" is about digging up dirt on employees in order to get them under their thumb and abuse them. Had a gf that got her desk rifled through, and sat down and talked to over her "satanic music" found in her desk. The company has the right to dig through a person's desk (the desk is company property), but the "satanic music" was just a heavy metal cd she had in her desk. She turned the tables on them and asked if they were saying that they were discriminating against her on religious grounds (ie: manager thought he "had her" by trying to shame her for listing to "devil music", when really from an HR perspective that means he was discriminating against her via religion.) Petty work environments like that are to be avoided if at all possible.
In the case of government work (or any other kind of sensitive job), the computer should be handled with kid gloves. You just have to work at a place to feel the environment out to see if they have a lax monitoring policy or a strict one. If it's super-strict, they will often have notices when you log in reminding you that everything you do is being monitored.
But, bottomline is.. just becasue they don't say you're being monitored doesn't mean they're not monitoring you. And, it's their property. Think of it like being in school again. The teachers can go around checking your locker, becasue it's school property. You don't own the locker.
If you have something serious to discuss with someone, and you're worried about it biting you in the rear, it's best to have a face-to-face conversation, that way an email or phone call can't come back to haunt you. Once you fire off an email, it's basically stored on a server and can get dug up to get used against you when and if the company / job deems it necessary.. even if it seems to be based on petty office politics.