Actually, she might have a valid case. What makes that so is that the E-mail account he read was a web-based Gmail account, and perhaps not a jointly shared E-mail account. The content of the E-mails are held on a server "somewhere" and not generally stored on the home computer, even if the computer itself is jointly owned and shared.
Other relevant issues not addressed in the article are:
1. What was their marital status at the time he read the E-mails? Were they still married? Separated? If separated, was there a separation agreement that addressed the joint use of the computer?
2. Did she previously give him permission to use that Gmail account and just arbitrarily decide that he no longer had her permission to use it and not tell him when that access became inconvenient/embarrassing? In other words, what was their past practice regarding that Gmail account and if there was a change was he notified of that change? Did she take any concrete steps to assure privacy such as changing the login password?
Using W2R's analogy of reading paper letters, if those letters were stored in a jointly owned home that he otherwise had legitimate full access to and he found them then of course she doesn't have a case. However, if she had moved out and established her own domicile that he did not have keys to, and he broke in and found the letters there, then she'd have a good case for a burglary.