[PHI 2200] Do animals have a moral sense?

According to Metaethical Moral Relativism (MMR):

The truth or falsity of moral judgments, or their justification, is not absolute or universal, but is relative to the traditions, convictions, or practices of a group of persons.

Now, experiments, like those showcased in this NOVA Science Now episode on Animal Morality, show that animals display moral and altruistic (selfless) behavior, such as sharing with others, helping strangers, and the like.



If these experiments really do show that animals have a (rudimentary) moral sense of right and wrong (e.g., a sense of fairness), would that undermine the thesis that there are no absolute or universal moral truths?