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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?
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.