While that argument may make no sense to you or me, it makes just as much objective "sense" as any other moral basis. Some people are strict utilitarians, some people have a deontological code, some people's morals come out of a holy book, and some people equate moral with legal. None of them are "correct" or "incorrect," and they absolutely do not make "sense."
The other systems you mention may or may not be arbitrary, but at least they're not circular. The reasoning "It's immoral because it's illegal and it's illegal because it's immoral" is unsound because it's circular. Disagreeing over your base set of axioms is one thing, but circular reasoning is quite another.
Under a circular legal moral system, moral progress would hinge on new understanding of old laws or else nominally morally neutral changes to the law. The other systems more easily promote moral progress via new understanding. Utilitarians can have new insights into utility functions. Religious based morality can have life experience and new cultural understandings influence their understanding and consequences of their basic commands.
