If the device is not locked, how about just launching the Mailbox app and browse the attachments via its fancy UI? :)
Because as far as I am aware, few mail clients either support or (if they do) actively encourage an extra password layer, and your users do not want it. Given an average un-password-protected phone, you will be able to read their email even if they were using the iOS encrypted files framework, just by opening the app.
I apologize, but it appears that your headline is deliberate sensationalism. If you want to have a discussion about how we need to secure email apps in general, I'm interested. If you want to just pick the latest 'big thing' and take pot shots at it, nah.
Of course, I am not highly versed in security, so if there's another option I'm interested to hear it.