I've read quite a few news stories that highlight this aspect of the story - it is, after all, the most interesting bit of it - but I think it's window-dressing. As far as I can tell, the Sunday Times was tipped off anonymously on Twitter, and when they asked Rowling/her publisher about it, they confirmed it was her.
Of course, that isn't a very exciting detective story, so if we insert a bit of mildly dubious computational linguistics into it, it works much better for the newspapers. (The analysts were essentially asked to confirm her authorship, not detect it.) I'm not getting the sense that this analysis needed to be done in order to force the admission.