In this case, a predator may been caught, but the incident also indicates that your e-mail is not as private as you might like it to be. Google recently failed to have a potential class action lawsuit alleging that it wiretaps Gmail dismissed.
As Google itself has said, “a person has no legitimate expectation of privacy in information he voluntarily turns over to third parties”. These words serve as a sobering reminder that whenever you place any kind of information into the hands of Gmail, webmail providers in general, or any third-party service, even for completely legal purposes, you can expect that the information may be seen by humans other than your intended recipient (or at least scanning bots). This includes apps such as Snapchat, which, as I wrote in an earlier post, Bruce Schneier does not think we can rely on to protect our privacy.