If you jailbreak the phone you can access all non protected data.
iOS Mail app uses DAPI correctly. For push mail when the phone is locked it will use a public key to encrypt the data.
I am unsure if even the Gmail app uses it correctly, I only tested the stock mail app.
If you have the an escrow key pair (ie. synced to iTunes) your are screwed. If should do a DFU mode restore to wipe the keybag completely.
Citation needed.
Then, even if the device is later locked, they can bulk copy unencrypted files using tools like iExplorer, and browse at their leisure.
It's funny how some business class apps store usernames and passwords in clear text in their app sandboxes.
If you can unlock the phone, you've almost certainly already lost here.
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.
I think most devices paired with an ActiveSync (Exchange, GMail) account are required to use lock codes.