It seems a rather disingenuous attitude on her part. I wonder why she showed it to the police if she didn't consider it actionable. Not everyone goes running to the police when someone says, "You will pay for what you've done."
I'm also surprised, given the language police see routinely, along with their knowledge of what is legal and what is not, that the police would suggest such a comment is a death threat. I find it more likely that they'd roll their eyes at someone bringing them something like that. I feel sorry for the Metropolitan Police if they interpret every remark of that sort as a death threat. They must be grossly overworked chasing down 'death threats' from ex-wives, ex-boyfriends, and angry neighbors who hurl unpleasant insults, send angry emails, and post nasty remarks on FB. I thought the police usually sort threats by 'credible' and 'bluster'. And that particular remark doesn't even really qualify as a threat. It's more of a prediction.
A more likely scenario is that she went crying to the police with a nasty email, some polite officer said something like, "Well, I see how you might have interpreted this remark as a death threat, but we don't act on this kind of thing" and sent her away. There was no police action taken, right? Now when she's asked about her police report, she's embarrassed because the police thought she was over-reacting, so she puts a little spin on the story. "Well, I didn't think it was a threat, but the police did." Only they didn't because they didn't act on it. And they wouldn't have even known about the email if she hadn't taken it to them in a paranoid tizzy.