A reviewer's IP address could be sufficient information to make a reasonable guess as to the identity of the reviewer.
To be safe, all peer reviewers should use an anonymizer such as The Onion Router (TOR) when searching for or downloading material related to a paper that they are reviewing.
TOR routes a user's traffic through intermediary nodes to disguise its source and destination from all parties.
(I sincerely doubt that academics are using their httpd log files to unmask peer reviewers, but one should not take chances.)
The real reason why it's important for academics to actually use TOR is that anonymizing networks are frequently seen as unnecessary for free, democratic societies.
The need for anonymity in peer review is one good reason to have anonymizing networks in free, democratic societies.
TOR also has an anonymous publishing protocol, and if TOR grows large enough, it may play an important role for whistleblowers exposing corruption some day.
Most importantly, anonymizing networks like TOR serve an important function for democratic activists working in secret against authoritarian regimes.
If anonymizing networks are seen as having an important function in free, democratic societies, then they may be able to grow more freely within them, and as they grow, they cast a wider net of support to those whistleblowers and democratic activists.