The way I see it is I earned that title. It wasn't class specific, after all. For me, I earned it on my mage, my mage who I hate playing now. Guess what, though? If DKs were around back then (well, as a playable class, at least) I'd probably have gotten it on that character too.
The thing is, I probably wouldn't even use it, but it would be nice to see it listed among all the other titles I have as it's part of my WoW history. This idea that I don't 'deserve' the title on another character because that's not what I earned it on is ludicrous. Once again, I earned that title through my own ability and perseverance in finding a raid of capable of doing the required steps. If it ends up not being available to my DK, well, that's fine but it's fairly silly to say that I shouldn't be "allowed" to have it.
---------- Post added 2012-08-12 at 05:03 PM ----------
Uh.. the person playing IS the person who got the achievement. Your character isn't sentient.