I know very few of the details about the affair regarding Chief Judge Kozinski and the web pages, but I have to agree with Robert Cooper at Screming Penguin that "Lessig is just wrong..." in his comments On privacy in the cyberage.
Part of the confusion, as I see it, is that too many people are getting hung up on the issue of technology. I think Lessig is correct to say that "[p]rivacy is not determined by technology". But this matter has very little to do with "technology", except perhaps for the fact that some people don't understand the "technology" and its implications.
As I see this matter, the problem arises due to a conflation in many people's minds of 'obscure' and 'private', though these are not at all equivalent. To be sure, in practice, something that is sufficiently obscure is almost the same as being private. If I publish a web page that no one ever reads, then the practical distinction doesn't exist, as my page, never being read by anyone, might as well be private. But in principle the two concepts are entirely different; if I publish in an obscure location, I may not expect to find a large audience, but if I publish something, no matter how obscure such publication might be, then I cannot reasonably assert any claim to privacy regarding what has been published.
Further, placing something on the web is publishing it. In many cases, such may not be publishing widely, and the publication may remain obscure and little-read, but it is nonetheless publishing. At least unless steps are taken to retain the priveleged nature of the information -- something akin to distributing a memorandum labelled "company confidential".
And this matter has nothing specifically to do with the Internet or the web. The same sort of thing has occurred before there was an Internet, when things written in some obscure publication came back to haunt their authors when they became known to a much wider audience in a different context. The Internet and search engines may make it easier for published information to leap from obscurity to notoriety, but the principle is no different.
That principle is that something that one has published is no longer 'private', no matter how obscure the publication might have been. Of course, one may retain various other rights regarding reproduction and so on, but one cannot reasonably be said to retain a right to, or expectation of, privacy regarding information that one has published.