I am sure Google checks something related to your domain name, could be the whois info, register date, etc.
I'm pretty sure they check whois - not sure why they wouldn't. They could use it to limit the strength of links passed between domains of the same owner. They may even consider (to a small degree) the length of domain registration, as spammy sites are less likely to register a domain more than a year out.
During a Google stuff up, i had 2 sites on different servers, different DNS and different everything besides Whois owners details. These 2 sites were different niche's, and had never linked or redirected to each other in any way. About a week before the PR update, one site got the cache snapshot of the other then when the update happened the domain with the wrong cache got the same PR5 as the other. A week after the PR update the cache came good, and it went back to PR2 which it should of been all along. There was absolutely no connection besides Whois, so it was obviously a data glitch during the computation of the Pagerank.
bank's story and stratcolby's explanation are convincing. Google could potentially do that. But my question is, would that be the best way to check for the same ownership of domains? If that is the case, I should stop using PrivacyProtect.