In protecting property the government is doing something quite apart from merely keeping the peace. It is exerting coercion wherever that is necessary to protect each owner, not merely from violence, but also from peaceful infringement of his sole right to enjoy the thing owned.
Now, at first this sounds silly, like a murderer complaining that he isn't free to shoot people. But it highlights a deeper point about freedom - recently noted at Left2Right - that a right of public access is no less a valid form of freedom than is a right to private property. Freedom to use common land and resources is restricted by private property rights, which replaces it with a (particular individual's) freedom to dispose of property, and exclude others from use of it. I'm not here arguing for one or the other, but merely pointing out that both forms of freedom have a prima facie appeal to them, and should not be overlooked. Libertarian rhetoric about government "interference" is thus misguided. As Cohen puts it:
The government certainly interferes with a landowner's freedom if it establishes public rights of way and a right of others to pitch tents on his land. But it also interferes with the freedom of would-be walkers or tent-pitchers when it prevents them from indulging their 'individual inclinations'. The general point is that incursions against private property which reduce owners' freedom by transferring rights over resources to non-owners thereby increase the latter's freedom. In advance of further argument, the net effect on freedom of the resource transfer is indeterminate. (G.A. Cohen, S-O,F&E, pp.56-57)
Thus the common rhetoric about freedom and government interference is not ideologically neutral. Rather, it presupposes that the propertied classes are entitled to their holdings. When this entitlement is put into question, it is patently question-begging to defend it on the grounds of "freedom" or opposing government "intervention". In ignoring the freedoms others would gain from the resources, you must be already assuming that they have no legitimate claim to them. But this is precisely what's at question.
Update: See also Poverty as Unfreedom and especially A Reasonable Resolution. The latter argues that taking non-interference as fundamental actually entails welfare rights.