And that's true of almost all moral structures - almost everyone claims that their system of morality is grounded in objective truth, with the possible exception of consequentialist systems. If you accept the axiom that God exists and He has made certain pronouncements about morality, then a theistic system of morality and ethics follows perfectly logically from that. If you don't accept those axioms, that system of morality will not be logical to you. In that regard, objectivism is neither more nor less rational than any other system of morality.