Aren't you forgetting the difference between private action and government coercion? Civil liberties as I understand the term involves freedom from the government. When the government threatens to regulate interactions between private parties, that's when civil libertarians should start getting worried. This is particularly true when the interactions are in the form of private communications.
The justification for the FTC's involvement here seems sparse. Websites can only learn about you what you choose to tell your web browser and communications software. Most people recognize no obligation to tell the truth when asked nosey questions by electronic snoopers--they lie to protect their privacy. Moreover, there are lots of private solutions to this supposed problem: You can use Anonymizer or Luckman's Anonymous Cookie to hide your tracks when cruising the web, and you can use encoding (e.g., Pretty Good Privacy-PGP) to ensure that no one misuses your e-mail. And as the Geocities settlement shows, you can enforce existing norms about consumer fraud and misrepresentation.
Let's not always go to Big Brother for the solution. Give freedom a chance to work.
P.S. The answer is neither.