The woman feels uncomfortable and checks the phone, then the man gets to feel uncomfortable about his personal privacy for the rest of the relationship...fair? Not to me.
They have this thing when cops investigate crimes, it's something Latin-y but translates to fruit of the poisoned tree. It's stuff that they find as evidence, but because it's not on a warrant it can't be used as evidence in court and basically can becomes moot. Personally, in my relationship I try not to do anything sketchy that would negate the results I'd get from doing it, know what I mean? Two wrongs don't make a right, and definitely set a pretty shoddy precedent for a marriage.
Girls lie when cornered too, the trick is not to "corner" anyone, but to open up a dialogue. To have a decent enough relationship where you aren't with a liar and don't have to force a decent person to get defensive.
Given the limited information we have, it's impossible to assess if she's being paranoid or if she has reason to doubt her SO. But in my opinion, that's kind of immaterial. Someone's past behavior doesn't dictate what their future actions would be. Even if he's a cheater, he could've feel legitimately bad for what he did, and the OP is now just constantly doubting him (not saying that's the case here). What matters more than what may or may not have happened is what the OP is willing to do to better her future, whether it be working stuff out or finding stuff out.
*jumps off soapbox* :)