Her looking through your phone means she does not trust you, is insecure for whatever reason and does not respect your privacy.

You've also blurred the lines of what is acceptable by having an "open phone" policy. Your phone is private, her phone is private - you either trust each other or you don't. You shouldn't blur the lines of what is and isn't acceptable like that. If someone is unable to be in a relationship with you without that kind of access then take it as a red flag and move on - don't enable behaviour where people act on their insecurities or continue their inability to trust.

And it doesn't matter if a partner has been burnt before - that is their problem and something they need to learn to come to terms with and move past. Taking that into their next relationship and holding their fears and insecuriteis over a partner is a recipe for disaster.

I'd be seriously considering moving on if I were you. You already went way beyond what is needed to show trust by having an "open phone" policy and she couldn't even respect or trust you then; she still went behind your back snooping, and tried to throw that in your face in an argument. This does not sound like a healthy relationship.