FWIW,,this is what I believe is the routing...
From your device to the carrier's tower (see the Host routing table in Advanced Options)
then to RIM's NOC via APN, or the carrier's VPN like setup.
then thru the internet via port 3101 to your firewall
then to your BES-->Router-->Dispatcher-->MDS where it is optimized then the request is sent to the internet
since the session should be stateful, it will(?) come back to your BES, be processed & optimized by the MDS and
sent to your device by the reverse of the above trail.
It seems the trail of data is HH-->carrier-->RIM NOC-->your FW-->BES--backout to the site-->back to the BES, process-->all the way back thru the cloud-->RIM-->carrier-->HH
So the Blacberry Browser will save you $$ depending on your data plan/carrier because the Internet one is not optimized, and flows lots more data, and the BB will be faster because the device doesn't work so hard.
OTOH, our infrastructure, BES and otherwise, is restricted and I can't see images on online storage sites, so the Internet browser is cool there, and I can use it. Your question is a good one. It made me think about the $$ issue. I may want to restrict use of the IB (for the hoi-poloy, regular users, that is.) 
