The registrar or the party who filed the UDRP? If it's the registrar, it's part of the agreement in case you didn't read it. AFAIK, no registrar is going to be a moron to lose their registrar accreditation for not following their agreements dealing with this issue.
If you are a site with a forum or blog then I really suggest using private registration. I speak from experience. I get harassing calls from trolls at all hours of the day and night.
Resistor domain on Netfirms dot com they are giving free privacy and also give 25MB web space & Email Address @ very cheap prices, 6$ USD, my all 7 domains are registered with NetFirms, service is good.....
Sure, you can add privacy later, but when you do this a lot of times the original information that you use when you register the domain is already saved on the whois database. There's a historical whois records so you can check all the times a domain has change the whois information. So if you plan to protect the ownership of a domain you better register the domain with privacy registration .. My 2 cents..