BYOD device platforms don't work that way... they are typically sandboxed solutions housed in an app (like Good Technology) or solutions which use the native email clients on the device via a separate device management and settings profile that handles things like SSL certs, enforcing password rules, setting up email settings and allowing remote wipe of the corporate data. There is no interception of 3rd party app data or personal traffic (e.g. sms, email to other accounts, etc.).
The one thing that is true and unique about Blackberry's platform is that they support many more device management features than iOS or Android. You can really 'lock down' a Blackberry with an ultra-paranoid device policy (preventing things like app download or even restricting usage of the built-in 'core' apps deemed unnecessary by the enterprise).
BYOD device platforms only allow corporate administrators a small subset of these features.