Quote: Either Blizzard's quest designers and story line people didn't communicate properly or the blade in question *cannot* be Ashbringer.
(and yes, I'm being somewhat vague for those people that have not played a DK as yet so they can see what happens at Light's Hope.)
Considering their past track record and that both of the quest lines that you listed would have had to be worked on concurrently for the expansion; I agree with Alliera that does appear to be intended to represent Ashbringer. The quest text in the first step of the chain makes it an even stronger case that they are in fact talking of the sword being Ashbringer.
And I have played through the Death Knight start up and there are a number of disconnects with the event that take place there and what you finally run into in Northrend. Following some of the games side line lore (various books, diaries and other trash nick-nacks that drop from mobs or part of quest line hand ins), there is a major time jump of many months from the last DK quest and when player are portrayed in arriving in Northrend. The best example of this is the two versions of "The Path of Redemption" that is for quests in DK starting area (7 pages long) and the Dragonblight version (24 pages long). Those extra pages give insight to what transpired from the time of the DK starting quest line and player coming to deal with the Scarlet Onslaught upon arriving in Northrend.
DK(7):http://www.wowhead.com/?item=39654#comments
DB(24):http://www.wowhead.com/?item=37931#comments
edit 01/01/09: Having just played through the quests in that area again on another toon, there is an emote from the action script that happens after the quest hand in. emote: "Highlord Tirion Fordring picks up the Ashbringer." That is pretty blatant as to what the artifact was that you were recovering.