Now the thing to notice here is that she uses it selectively. The first two lines we hear clearly:
No matter how hard I try/You keep pushing me asideare sung without Auto-Tune as is evident from the perfectly normal vocal expression, sliding from one pitch to another on "how" and "try". The next two lines use Auto-Tune because we can hear the software forcing the voice to jump abruptly from one pitch to another instead of sliding as is more natural. These contrasts are what make the song work. Now let's listen to that song by Bublé:
Wow, does that ever remind me of Paul McCartney! Not so much the singing (I don't think they are in quite the same league), but the arrangement, the kind of melody, the whole feel of the song is rather McCartneyesque. I don't really hear the singing as being "positively inhuman, devoid of DNA". If he is using Auto-Tune, which is quite possible, he is using it to correct wobbles, not for effect. But the thing is, if you want ANY vocal expression that involves bending the pitch at all, you have to back off the Auto-Tune for that section.
Incidentally, there are quite a few comments to the article that make some good points. But the truth of the matter is that, just like a lot of the technical innovations of the Beatles, it is all in how you use it. I'm afraid that I don't hear much of a creative use of Auto-Tune. The Beatles were constantly coming up with things like ADT (automatic double-tracking) to improve the musical effect. Yes, they liked to double track vocals as it gave them a lot more presence. This is very time-consuming so one of the tech guys figured out a way of doing it by just delaying the signal a bit. You know, I think Bublé could have used that to good effect here. Don't you find his voice a bit thin?
Let's hear Paul with a somewhat similar song: