Belief is the acceptance of a statement (or system) as being either real or true. In this usage, we'll consider "belief in a government" to cover the following, "The acceptance that a system of government is an effective means by which to manage a group of people living together."

So to believe in a system of government, you must therefore accept that this system of government is the most effective way by which to manage a group of people. If you believe this, then you necessarily must believe that to break the rules of this system of government is to introduce a less effective means by which to govern a group of people. It's simply the inverse of the belief.

If you believe the US government is an effective method of governing a body of people, then you must believe that to move outside of the system is to be less effective at governing a body of people. In its strictest sense, this means that you believe in every law and every process by which these laws came into being. In a more realistic sense, you understand that a body of people will want different things amongst different internal groups, and a government's job is to balance those wants and needs against one another.

Edward Snowden broke the rules of the system of government. If you believe the US government is effective, then (because of the argument outlined above) you believe he has introduced inefficiency, and is making the governing of the people of the US more difficult.

So when you say "people do [believe in a system of government and also act outside of it ]" you are incorrect. The act of moving outside of the system demonstrates, as outlined above, a lack of belief in the system of government which is being acted outside of.

Anyone who breaks laws as a means of enacting change does not believe in the incarnation of the system of government for which they're attempting to change. Martin Luthor King Jr. Oskar Schindler. Timothy Mcveigh. Osama bin Laden. Every one of them attempted to enact change by working outside of the system in which they were attempting to change.

It should be an indication to you that you find such an idea to be negative in the first place when Snowden is brought up. Why exactly do you think it's so negative that I say he doesn't believe in the US system of government? Perhaps because what he's specifically done in terms of actual policy change could have been accomplished without breaking any laws?