Just like with everything else about Google - it should be pure logic (I hope).
The logic is that rankings could change if the content has changed, like Tedster pointed out.
The logic also is that rankings could change if the new owner is an entity marked as a blackhat, spammer, or whatever.
On the other side, if business is as usual, and Google is not suspicious about “so and so” site, there should not be rank change after WHOIS has changed.
I think that although privacy option can be abused and misused by domain owners, it should also be respected.
All of my domains are registered through a company that does not allow company name to show as legal owner (although corp is the real owner). In addition, they do not allow PO box to be used.
Well, since I work from home, I don’t want the address where my kids resign to be out there in the “here you are” fashion. One could say "rent an office", but working from home address is such a reality today which cannot be ignored or blamed.
I hope that Google is using a common sense in this case.