I think it's the "external" part of the phrase that's a problem, not the "multiple". She could've sent it to one external party and that still may have been a fire-able offense.
(Of course, this depends on what she was sending, if it was really protected information, and who she was sending it to. If she was sending evidence of criminal wrongdoing on the part of Google to her lawyer or a government official, then I don't know).
I don't have Google experience, but you can be summarily fired for forwarding to a personal address at many companies with a security or compliance policy. You would have known this in advance, whether through training, a manual, or warnings inside the email client.
I remember an all hands where someone forwarded a relatively innocuous email to her Yahoo, once, and we all received a big reminder.
It’s true that companies don’t like that. It’s also true that common advice to people experiencing some kind of workplace harassment or abuse or bullying is to follow up to verbal conversations in writing, and to keep your own copies of those documents in case the company decides to accidentally delete them before they get a subpoena or whatever.
So a question is then whether it’s morally sufficient for someone to be fired for this sort of behaviour. It feels to me like the reason for the firing was not really at all related to breaking the written policies in the company handbook and a lot more related to breaking the unwritten policies about stirring up trouble and dissent.
(Of course, this depends on what she was sending, if it was really protected information, and who she was sending it to. If she was sending evidence of criminal wrongdoing on the part of Google to her lawyer or a government official, then I don't know).