Surely (in the OP) they are assuming that the letter was headed with your address and the Bank used a window envelope. Maybe there is cooperation in the industry to send statements (etc) uniquely this way.
FWIW I shred everything that has my name/address on it, and a lot of crap that is just advertising has my details on.

I bought something from John Lewis and it needed to be returned under guarantee and they said they couldn't trace the sale. The on-line (only) credit card record only went back 6 months so I had to pay 5GBP for a statement just to prove John Lewis had not charged my credit card! So it wasn't guaranteed after all!