The claim that morality can only come from God, that there are no rational secular grounds for morality, is a large claim. God might say, for example, that we should eat fish on Fridays. He could just as well have told us to eat fish on Wednesdays, or eat turnips on Fridays. We have no reason for following them other than that God commanded them. Indeed, if God had commanded the opposite, we would be morally required to kill, steal, lie, rape, or whatever God commanded.
Secular morality CAN be objective.
Some definitions, from Webster's Collegiate Dictionary, 10th edition. These are two different uses of the word, which must be kept distinct. Objective things can be relative, subjective opinions can be held absolutely. When he says it is universal and unchanging, it means his morality is indifferent to the consequences of trying to follow it in the real world. He may also mean that he is willing to apply whatever force may be necessary to make everyone else bow down to his own chosen Lord.