I am in an industry that has lots of compliance rules
There are BYOD solutions that meet the requirements. The BYOD security models are no different than the non-BYOD (e.g. Blackberry) security models.
Don't forget that when you're using a VPN connection, that's a BYOD device, typically. Most times employees connect to the company VPN with their home PC.
The security strategy of BYOD solutions are no different than that of a VPN client...use strong encrpytion for data in transit, protect/encrypt data at rest, and make sure the right controls are in place over both authentication and the communications channel.
I think folks believe that BYOD means doing web-mail to the company email system and suddenly downloading spreadsheets and docs to their iPad for editing....it does not work that way.
BYOD devices (using an enterprise-app to manage them) have the same or better security controls than non-BYOD devices.