Every time someone writes a cheque or uses a debit card they're revealing the sort code and account number for their bank account. It's hardly privileged information!
It's normal practice for benefit providers (whether that be the DWP, local authorities or any other agencies) to require claimants to provide bank statements, etc. In some cases they can also insist upon making home visits. (e.g. because I'm registered as self-employed, even though I only do a few days work here and there, I was required to admit a DWP employee into my home, for a detailed interview, when I claimed Pension Credit).