Okay, somebody tell me why Internet access is not properly locked down
As a consultant, I often work in banking environments.
In one of those, Internet access was not allowed from the desktop, but you could launch an Internet Explorer session which connected to a VM that allowed to go on the Internet - except you could download nothing because the VM had no access to your PC. It seems to me that this is the solution to that problem.
This solution is probably not easy to implement, I have no idea since I'm just a lowly programmer and not a sysadmin, but dammit somebody has found the solution, so it is possible. And knowing the bank in question, it likely did not cost an arm and a leg to set up.
So let's get cracking. Forbid everything from the Internet, create a sandbox environment that can access Internet, and this kind of problem is gone.