Jeb is trying to look like he is being transparent and open but it is a sham since he has no choice. The correspondence is, by law, public information.
From the Governor's web page:
"Under Florida law, all correspondence sent to the Governor's Office, which is not exempt or confidential pursuant to Chapter 119 of the Florida Statutes, is a public record. All public record electronic mail sent through this website will be posted to Project Sunburst at www.flgov.com , and will be accessible to the public. If you do not want the public record contents of your e-mail or your e-mail address to be published on this website or to be provided to the public in response to a public records request, please do not send electronic mail to this entity.
Please be aware that personal information sent in your correspondence, such as home addresses and telephone numbers, may be posted to the Sunburst public records website."
If your email sent to and from your office computer is open to your employer, the same should apply to the governor and all other elected officials.