I think this is a story that has been seriously taken out of context. The problem with stories is that the message is in the telling, and the telling tells you more about the person telling the story than the person whom it is about.
Even if the facts are exactly the same, the way a story is told can give it a very different meaning. And even the facts are usually completely twisted. For example, I heard it was some kind of cake and it was Rav Shach.
Actually, Rav Chaim Kanievsky Shlita doesn’t even speak to girls – he won’t even read a girl’s handwriting. Only on rare exceptional occasions has he spoken to girls, and that was only with his wife’s request.
Therefore, I don’t think the story has any truth to it.