Personally, I don't think you should have to mention anything else to her.
I think the main concern is that, why is she so protective of her privacy. My boyfriend knows everything about me. If he went online and looked up what I was doing online, I could care less. He could see the emails to exbf's and anyone for that matter. We have no secrets from eachother.
Sounds to me like she has something she's trying to hide, or she wouldn't be so freaked out about her ex or you for that matter looking at what she did online.
Every man who's ever kept secrets from me, has turned out to deceptive and didn't work out. Every man I've had secret's to keep from them, it never worked out.
I'd start asking her why she's soooooo damn protective of her privacy. You're obviously living together???