"Or" pulls double duty. Evidently, if you asked my college math professor "Would you like coffee or tea?", his respose would be "Yes, I would."

So if you're talking about a decision between a number of alternatives, then that is exclusive by understanding, I agree. But when you're talking about the connective between logical statements, it's not so clear to me. For example, consider "You should change the oil in your car every three months or three thousand miles." One would not conclude "I don't need to change my oil because it has been a year and eight thousand miles since the last time I changed it."