Are there any NACHA rules regarding this and authorization?
NACHA says nothing about "2 signatures required" accounts and ACH authorizations.
If your bank is going to continue allowing customers to open such accounts, you should be covering yourselves in your contract. Spend the money to get some legal advice, and ask the attorney about ACH and other sorts of electronic transactions. Don't forget to include in that discussion bill payment or account transfers using online banking.
Once you start this discussion, you may come to the conclusion that you don't want to continue managing such accounts, because there are so many holes in the sieve. In the meantime, I hope the bank is getting enough fee income for the added monitoring these accounts require.