In the case of Debian, it tells them you are using a specific version of iceweasel, which probably is quite deterministic in combination with the rest of the dragnet.
Whenever a new version of Iceweasel hits the repos, a bunch of people upgrade, and perform identical requests. You can figure out how frequently someone checks for updates I guess, but other than that what would you learn? The browser hasn't had the chance to acquire any information that would distinguish you from any of the other Debian users yet.
