I'm not saying this is always the case in the EU, though. Obviously there is equipment where for many reasons it's absolutely vital that you don't use it for anything personal. I'm not supposed to run a torrent client on the company server, for example. You can't just "borrow" a company car for a personal trip. But when I happen to use the laptop that the company has assigned to me to work on, to do a bank payment, my boss has absolutely no business knowing the details of that transaction.
I would be okay with them knowing I visited the banking site on company time (if I used their equipment, their DNS, etc) but not with decrypting the SSL encrypted data I'm exchanging with the bank or obtaining it in some other way such as a keylogger.
Though again, I'd probably avoid the issue entirely by using my own device and data connection if I didn't trust my employer. (I'm a bit spoiled, working in IT: I'd probably know if my employer was doing shady things with the data)
How did this work? I presume they had a whitelist of Internet banking sites. But, do you really think their whitelist would include every Internet banking site in the world? I doubt it.
Still, I just... would never feel "entitled" to use my employer's property for personal uses. And I wouldn't have an expectation of privacy. When I care about privacy, I simply use my own device.
Now, let me be clear. The reality of working in America is that people use their work computers for personal uses all day long. Generally nobody cares, as long as you're getting your work done.
And if somebody really needs to do something personal, they can always just whip our their phones. If I was printing out some concert tickets at work, I'd use my employer's printer. Everybody does this. But if I was going to send some sexy messages I wouldn't do it with work equipment.
So, I don't know. I just don't see the problem. There are many many problems with America, and many ways in which Europe does things better IMO. I just don't see this as one of them.