If someone actively looks through your phone just to snoop, that's fucked up. I would have problems being with a woman that constantly did that. Sure, you shouldn't have anything worth hiding, but she shouldn't distrust you enough to look either.
However, realistically we all use the other person's phone for shit occasionally or see texts pop up, and that's normal. I can't imagine how that has never, ever resulted in his wife seeing something she shouldn't have, with how long he has been doing that.