Just to clarify, the issue is 'BES' not 'BIS'. Blackberry Enterprise Service vs. Blackberry Internet Service. BES is the corporate server, whereas BIS is just straight e-mail through blackberry.
You need to get all the policies from the BES administrator. I don't believe there is a way to see a full policy dump from the phone.
BES was designed to do everything you are asking for to 'protect company data' from unauthorized access and release. Just wasn't designed to work with multiple companies on the same device.
A third party IMAP client doesn't really help if you're connected to a BES server as the BES server has the ability to see everything on the phone. If the datastore for LogicMail's IMAP client is encrypted, technically, the BES admin's would have access to the datastore, but may not be able to access it without a password. If 'disclosure' is the concern, I think one would be able to argue that the corporate e-mail server is no different than a transfer medium and should not be considered 3rd party disclosure.
I'm in the legal world (from the technical side), we have over 100bb's issues to employees with BES and this has never come up. Phones get lost all the time though; its great to know they are locked, encrypted, and we can wipe them remotely.