I noticed this feature does not work completely. For domains I registered recently with dreamhost it is fine. For domains I transferred a year ago it only works to change the registrar. I am still listed as the registrant, administrative, technical and billing contacts.
To check your sites thourougly you need to search on the network solutions site at
Other whois sites usually only show the registrar, so you may think it is private when it is not.
I have emailed dreamhost for a solution and have not yet had any success - they say it is private when it is not. I have pointed them to the NS whois site and am awaiting another response. I will post an update when I hear back.
I do like dreamhost in any case - they have been great.