I don't think you offended anyone, especially not me. My statement might have been a little harsh, I sometimes seem to do that, but the reason I made it is because I consider the rulebook and FAQ to be the highest authority of the game. They are THE official statement. Thus, I didn't see the point of asking a question again when the documents had answered it. Shad0w's statement may help to alleviate your debate.
Thinking about it, I suppose I can understand your groups confusion. The rules on page 24 are quite clear that the creature can not use more than one defense, so it seems your player's are probably trying to argue that the Mage has yet to actually use a defense themselves. The Dancing Scimitar card does not state that the Mage gains a defense like other similar cards do (Reflex Boots for instance), and between the Codex and FAQ it is clear that thematically the Scimitar is acting independently (even though it must follow the Mage around).
Thus, I think we can all agree thematically that the defense originates from the sword. It is the one doing the work and actually creating the defense. However, the question isn't regarding where the Defense comes from, it is regarding what is using the defense. The word use has several definitions, including "to exploit," "to avail oneself of," and "to apply to one's own purposes."
And so, if they want to say that it is the Scimitar that is acting to create the defense, I will agree with them. If they want to say that the Scimitar used the defense to protect the Mage, I will agree with them. If they want to say that the Mage did not use the defense to avoid getting hit, I will have to disagree. The Mage clearly made use of a defense and thus the Mage can not make use of another defense against the same attack.
I hope that with that logic, the rules on page 24, and the official word from Shad0w, you can put the issue to rest and finally quell any dissent within your group.