I see your point jag... i know i shouldn't check it, but isn't it kinda human nature to wanna trust someone... and if the means of proving it to yourself manifests itself (ability to check email) wouldn't one wanna do so?
Judi is wrong.
Save yourself some hassle and boot this chick.
You were wrong for checking her e-mail as she was for lying about contact with an ex. Two wrongs don't make a right.
I'll give her the benefit of doubt and say the obligatory "there's probably nothing going on and she didn't want you to make a big deal over nothing". Even put in the best light possible it comes down to the fact that if she'll lie about this, there are other things she'll lie about too.
My GF has the password to e-mail, credit cards, computer, etc... because there's nothing to hide but I also don't lie about crap.
You're probably young and won't listen but some day hindsight will clearly show she should have been booted.