When the Dragon Hunter quest is completed, you get a popup advising you that the quest is completed, same as you get when you buy all the beds or what have you. Could that popup not write an entitlement to your account as well?
Not when your playing the game offline, or if your internet connection disconnects during game play which is why aquiring it through SP means can't really work, unless the unlock is built into the actual game itself. Also from what the member of staff mentioned it writes the data to the multiplayer account not the main one.
Unlocking it through killing all 10 dragons isn't an option either since most MP players also play SP and have likely got that achievement too and by making it connected to that would prevent them from acquiring it through MP if they preferred. Don't the MP players have a website for accessing their multiplayer data regardless of what console they got to play it on?, believe it's inquisition HQ, if that can access the data, then surely the data can be written to it too making it the ideal place for a web based option to get the set?
Also I think they might avoid providing the set as a DLC since it would mean they would have to back down from their refusal to make any more DLC's for the PS3 and Xbox 360.