BOI statement

I doubt it, security is very strict these days and staff are only allowed to access data that is necessary for their daily work. So the idea of a random clerk in a branch being able to access and print out your statements is very unlikely. Occasionally people have a specific member of staff assigned to them and it appears somewhere on the statements, now if you were to go and see that person or their supervisor, I'd expect they'd be able to access your statements.

You don't mention the periods you need the statements for and this is key to the time line. Somewhere in your T&Cs the bank makes you responsible for keeping copies of your own statements and so they quickly take old data off line to save money. So if you're asking for very old statements, it may have to be requested from some off site storage location, loaded on to the computers and then printed.