Anarcho-capitalists advocate private courts and private enforcement, but that is impossible (at least for cases like this one) to put into practice when an existing government has already established a monopoly on this. Unless the government is abolished, using its facilities is a perfectly reasonable way to settle conflicts. Not only that, in some cases, using government facilities becomes mandatory, whatever your political beliefs. For example, if someone gets murdered in his house, and he is the sole witness, he is bound by law to report it. (At least, this is how I understand the law.)