This is based on paranoia, but I'll ask the question anyway. Is there any reason (or logic) to believe that registering a domain privately might affect a site's ranking in google?
Registering a site privately and keeping it hosted elsewhere, along with zero links between the site and others you might own, could hide the fact that an individual is trying to dominate a serps.
Having said that, maybe google doesn't care about one person attempting to dominate a serps as long as there is no "artificial attempt to boost a site's ranking in google". In other words, as long as the sites get their own backlinks.
Anyway, any reason (or logic) to believe that registering a domain privately might affect a site's ranking in google?
Do a search for "googleguy whois" ... From what I'm reading you're better off not going private. Oddly enough I went private in February ... and I died with the June 27th update .... whether those are related... I don't know, but I'm terribly paranoid now.
From what I remember Matt Cutts saying, anonymous whois details, on their own, are not a problem. After all, there definitely are many non-malicious reasons for protecting your whois information. A lot of well ranked sites are registered anonymously -- so on its own, anonymous whois data is clearly not "the kiss of death".
However, coupled with other negative "points" raised by a domain's activities, an anonymous whois can be the one final negative factor that puts a domain over the top and trips a punitive action.