I would definitely want to find a different bank. If they're that nonchalant about you "finding" 16K, they're likely to be the same about losing it... and since that 16K probly got entered to your account from a keystroke mistake, there's somebody out there whose account *didn't* get the dough... and one of these days it would come back to haunt you.
It could come back to haunt you somehow anyway, so I'd get my dollars *outta* there. What if they figure out the 16K - but *don't* figure out that you gave it back because they didn't record that in the same way? They'll be coming after you for it!!!