Inside the browser, I was able to select "Internet Browser" where it had been set to "BlackBerry Browser". I then exited and started up midpssh, logged into my Linux server, and found that I was still logged in as if coming from my Exchange/BPS server.
I'm admittedly no expert in Blackberry's. But I can't help but wonder how changing a setting in the Browser program would affect how a 3rd party application accesses the Internet. I'm not trying to "browse" my servers. I'm trying to get direct secure login access to them.