[michaelhoffman]

The old-school way to document savings accounts is with a passbook:

https://en.wikipedia.org/wiki/Passbook

If this bank offers that, then you have the redundant documentation yourself.

[iLoveOncall]

That doesn't seem like the kind of redundancy that the bank would trust. It's nice for you to see what is in your account but you cannot reconstruct a trusted bank ledger from those.

(but I may be wrong, the wikipedia page is short in details)