When effects trigger simultaneously, who gets to choose the order in which they will resolve?

The active player, the one whose turn it is.

That seems to contradict Mr. Hata:

"If you have a Dragonmage with Gromril Armour on it, and 10 points of damage are assigned ot it, then you choose in which order the two abilities resolve (this is because you control both cards and they work on the same timing). Therefore, you can have Dragonmage cancel all but 1 of the damage and have the Gromril Armour cancel that last point of damage."

Context is everything. We assume that DM is defending, but James may be assuming he is attacking. It is also possible that the controller of the effects makes all decisions, which if I was going to draw an inference from this clarification, it would be this.

If I remember/understand things you can either play something in response to your actions, in which case the last one played takes effect first, or you can play a card and have it resolve and then play the next one.