Yeah my bank is the same. I could download the statements, not sure who really does that accept the extremely paranoid.
Civil claims are based on a preponderance of the evidence. if I go into court with a piece of paper from the bank saying that I have $5,000, and the bank has nothing to say that I do or don't have any money there, I have more evidence on my side than they do on theirs.
But even if I did, what do you do from there? Call someone and say "I have a piece of paper that says I should have $x but they say I have $y"?