Simply put, the tragedy of the commons revolves around the use of a commonly-owned resource to create private wealth. Since each person wants to maximize their own wealth, they would naturally tend to increase their usage of the resource. This leads to an accelerated extinction of the resource. The only way to solve this problem is to limit each person's access to the resource.

The example of the Swiss cheesemakers is simply an example of how one group worked to limit each person's access to the common resource. I don't know the details of this agreement, but it would seem to pre-date the current government. I would guess that, in order to be effective, there is some mechanism for enforcing the rules of the agreement. I would also guess that it has been formalized to the point where violating the agreement opens the possibility of a court case – which would mean that it ultimately relies upon government power to make it work anyway.

At any rate, “governments are instituted among men” to protect rights, both individual and common. What the cheesemakers have done is establish a governing body of very limited nature. They didn't escape governmental actions at all, they just exercise them directly.

Beyond that, all government is simply a series of agreements by which we manage our commons, of various kinds. That's why politics is so contentious – we are all fighting to get our share of the commons.