First, I guess you have to decide if you really (and I emphasize REALLY) want to do business with this company.

Second, you could re-visit the conversation with them something like this:

"Thanks for pointing out "confidentiality issues" with sharing slow/no paying customers.  We have decided that OUR new company policy is when an account becomes deliquent, we automatically file a "theft of services" complaint at the local level.  That way when the police end up at a client's door to investigate the complaint, we feel in all confidentiality, that the client can explain it to the police.  Again, I sincerely appreciate you bringing to my attention that using the law to collect on deliquent accounts is the best way to let the world know that a business orders work from others, but does not pay for their order"

Ok, you'll probably not get them as a client, but seriously, do you care if this is their attitude with you?

The other alternative is to have them put up a retainer with you, that you draw off of everytime they have an order.  I'd say a $2000 reloadable acount when it gets to a balance of $500 is fair.

Attorneys do it ALL the time - lol

Best of luck in this particular venture!