The records in question are log files created by the schools' proxy servers of what URLs are accessed by the student body. The school district in question isn't censoring Internet access with any sort of censorware product (they use teachers to monitor what students are accessing), and the parent would like to prove that the students are accessing porn sites. I do not believe it is an invasion of privacy to access these records; if there was an invasion of privacy, it occurred when the school district collected the records on their students, not when someone else requested to see them.
Some comments of mine that didn't make it into the Times article: I hope that this situation casts some light on Internet usage at public facilities. Many, many Internet services are set up to create detailed log files by default -- proxy servers, Web servers, various login mechanisms and authentication mechanisms, etc. These records are being collected, and they are just lying around on machines or tape backups here and there, and they are, if the entity that collected them is a public entity, public records accessible under FOI laws. If you want to prove that your local school/library shouldn't be censoring the Internet, request the records. (I'll help! E-mail me.) If you want to prove that your local school/library should be censoring the Internet, well, I won't help, but I still support your right to get access to public files.
And while this situation is about records collected by public entities, the same records are routinely collected by private entities as well. Is your Web access going through a proxy server at your ISP? (The answer is more likely to be "yes" than "no," by the way -- a proxy can be installed that is transparent to the end-user.) Then your ISP is collecting detailed records of every single URL you access through their service. How long are these records being retained? Who is the ISP selling them to? Do you know?