Well, obviously, that's how he knows it, don't you think?
Jokes aside, while an average GTVA citizen might suspect the military isn't telling everything, most would probably go "well, it's not like we have anything better". Sure, people would suspect propaganda, but are likely to be rather apathetic about this fact. You either believe what they tell you and accept their version of events, or you don't, and accept the fact you know nothing what's really going on.
It would probably depend on what the agent would reveal. If he'd only reveal the military isn't telling the whole truth, the situation be like with Snowden. Some would be outraged, more savvy ones would go "Well, duh!", then it'd quiet down. But if he told
what the military wanted to hide, there could be trouble. Remember, Snowden mentioned he knows much more than he revealed, but he didn't want to release this info, because that would endanger people. If a hypothetical HOL agent wouldn't have such reservations, a lot of things could happen. And some people would die, probably, because there's a good reason why military secrets are so closely guarded.