i think that a lot of people are missing the point on this one.
i'm not a religious person, but one could view anarchism's critique of liberalism similarly to jesus' critique of the jewish law. liberals have this wide swath of rules meant to govern how states and people interact with each other. anarchists would say that there is but one simple rule, articulated in a wide variety of manners, but here in the old english saying: 'an' it harm none, do what ye will'.
but can any of us cite an example of a human right (not related to private property, in a traditional socialist definition: means of production, land, etc) that we explicitly disagree with? i would claim that we mostly cannot.
regarding natural law, let's take a step back to where it came from. we've all become very confused about this. for, aquinas would never have claimed that the natural law is an ethereal force or an authority. to the contrary, he would have claimed that it is to be arisen at individually through reason. aquinas' concept of natural law - which early liberal and anarchist thinkers wholly adopted - most closely resembled what we today call secular humanism. anarchists may be moral nihilists, but it is merely a step in reasoning rather than an end of it. we may reject absolute morality, but we would not reject our own logical intuitions as to what is just and what is not. we just claim that it is a human construction, arisen at through reason and carried out not because we are forced to but because we want to.
there are two kinds of rights: rights that individuals have in opposition to the state and rights that humans have in opposition to each other. in the first case, the fundamental issue is property. the right to food is about property. the right to shelter is about property. after all, the purpose of the state is to protect property. anarchists are consequently going to have a hard time with these kinds of rights, because we neither believe in the state nor in property. we would rather abolish both, and the rights laws that come with them, than accept the hierarchy they put in place. but, none of us would claim that we are not all entitled to food or to shelter.
in the second case, a moment's reflection is required: we would not have so many court cases in front of us that attempt to rule on human rights if we did not have so many violations. and, the underlying issues are often very deep seated. i think that anarchists should view this class of rights as an experiment. what it's doing is slowly putting in place the framework that we will one day adopt, when we are ready. it would be nice to claim that we do not need this - but, unfortunately, at the moment, we clearly do. we cannot abolish hierarchy overnight. there's not really a way around this in the short run - an anarchist society would need a tort-like system to deal with personal conflicts until the proper behaviour becomes enforced as social norms.
so, it's really a very subtle point. and it reduces mostly to the issue of property.