Even if relativists are right that cultures differ radically in their basic moral values, so what? The observation in itself proves nothing, because no conclusion about morality follows. Just because cultures differ on moral viewpoints doesn't mean that objective moral truth is a fiction. In logic this is called a non-sequitur; the conclusion doesn't follow from the premises.
Observations about the practices of groups of people, even if accurate, don't translate into valid conclusions about the true nature of morality per se. How does it follow that because each group thinks it's right, therefore no group is correct? The simple fact of disagreement on morality doesn't lead to the conclusion there is no moral truth. This confuses the epistemological question (the accurate knowledge of objective values) with the ontological question (the existence of objective values).
Currently there are conflicting views on many things. The fact that there is disagreement, however, doesn't mean that no view could be correct. The same is true with differences of opinion on morality.