Some of the agreements I have signed with these various registrars is that I will not divulge proprietary information that includes their clients and contact information. These logs include this information.
Since the registrations identifies both the client and the registrar and it is publicly known information, it seems like a meaningless clause to put in a registrars contract. I would think that the various registrars would know who their competitor's clients were by using their own methods and would not need to rely on you for the information. Have you asked the registrar that requested the information if they have a non-disclosure contract for you to sign? If they do have one, then they should respect your obligation not to disclose the information from the other registrars.
Isn't there a famous saying about "first, let's kill all the lawyers"?
Bill Pflanz