I understand that live performances often reveal the amount of technology that is involved in the recording process--pitch correction software is very sophisticated these days--but their latest studio album has her singing very out of tune as well, and I personally find it very distracting.
Having said all of that, I'm a big Sleater-Kinney fan, and nearly everything about them is way out of tune:
An accidental choice cemented Sleater-Kinney’s sound. In her previous band, the guitar-and-drums duo Heavens to Betsy, Ms. Tucker had only tuned her guitar to itself. When she joined Ms. Brownstein in Sleater-Kinney, they ascertained that Ms. Tucker’s guitar was tuned with its lowest string at C-sharp, not the standard E. They decided to both keep that tuning, which happens to push Ms. Tucker toward the topmost part of her voice. (Jon Pareles in the New York Times)
Furthermore, Corin Tucker doesn't really sing in tune either:
In the classical realm, of course, it's all about playing in tune: you basically can't get a job if your intonation is bad. Poor intonation is one of the reasons that Florence Foster Jenkins is so amusing to us:
(Perhaps it's something with the name Florence?)
It's interesting to think how attention to intonation might be characteristic of a musical style or genre. I suppose one could make an argument that Florence and the Machine should be forgiven the singer's poor intonation because it's part of the aesthetic they're after, but it doesn't sound right to me in the same way that Sleater-Kinney's intonation does. And Florence Foster Jenkin's intonation, while quite bad, is more likely to induce laughter than revulsion, I think, perhaps because it's so diametrically opposed to the aesthetic of classical music.