seriously though, surely this would just be one of many potential red flags that could be raised ... if you are up to no good with a network [as far as the search engines are concerned] this would be one of many indiators that they could use.
... but lets face it i don't think it could be that important because some people have been hiding their identities with false whois information since the beginning anyway
There are many legitimate reasons why someone might prefer private registration, so ordinarily it's a neutral factor.
However, if the site was doing things that got red-flagged for other reasons, private registration would be viewed more suspiciously.
In determining whether a person has a bad faith intent described under subparagraph (A), a court may consider factors such as, but not limited to:
(VII) the person's provision of material and misleading false contact information when applying for the registration of the domain name, the person's intentional failure to maintain accurate contact information, or the person's prior conduct indicating a pattern of such conduct;