I hardly ever deal with my bank face to face. Whatever I need done, I do by phone and have done so for the past 8 years. They've tried moving me to PC-banking, but that's not coming anywhere near my machine.
So... today I have to transfer some money to germany, to an account of someone of whom I've bought something through ebay. I walk over to the nearest branch of the bank where I'm a client and end up standing in front of a closed door. Apparently they ain't open on thursday afternoon, unless you have an appointement. Nice. Of course I don't have an appointement, how the hell am I supposed to know? I guess I'll have to try my luck again tomorrow morning and see if they can do this transfer.
Funny thing is, that even with Europe having one currency, I bet they still charge a lot for transferring money abroad, and I'm pretty convinced they'll tell me this : sorry ServMe, but we can't execute that transfer from this branch since you're not a customer here. You'll have to go to your branch 10 kilometers from here so they can do it for you. To which I will reply : "I'm a customer of this bank, this is a branch of that bank and I ask you politely to transfer that money for me".
If they insist they can't/won't do it, I'll ask for the full coordinates of the branch, the name of the branch manager and send off a "nice" letter to the corporate branch in Leuven. I've got all the coordinates right here with me. And I'll put them in CC.
Yes I know... I'm a badass customer :)

I've never heard of branch-specific draconian banking like the kind you describe, but I've done it all online for a couple of years now, so things could have changed.
I wish you the best of luck, and I hope you don't have to send off that 'nice' letter (well, secretly I'd like it to happen anyway. stick it to the man!).