Does anyone really care about achievements that much - is this what gaming has been reduced to? The pursuit of points or trophies? Whatever happened to just having fun?
Yes. Some people have fun getting achievements.
Heck, in my case, I don't even care about hunting achievements, but I do have a problem with not getting achievements that are rightly deserved. I think you would be annoyed if you were doing a quest and then the NPC you needed to talk to suddenly disappeared, denying you your reward.
But don't you keep the star with either choice, meaning you still get an artifact, and Azura is one of the Princes that isn't totally evil, so it would make sense.
The game could just as easily let you keep X artifact but without its evil daedric properties and count that as "complete". Like, an unpowered mehrune's razor, or an unpowered staff of nightmares.