The only dubious thing is how are people who install Alexa toolbar representative to the population as a whole. Do they collect some personal info, so they can correct the bias in the sample?

Yes, if you do shoddy analysis of your logs, your logs are wrong. Spoken like an Alexa-zon employee. If you know what you're doing, and recognize the assumptions that go into proper log analysis, logs are a much more reliable tool than a panel.

The only useful thing a panel gives you is a supposedly fixed standard for doing competitive analysis... same methodology used across multiple sites. But even then you have no guarantee that the sample is representative. This is why companies like Comscore and Hitwise who buy under-the-table clickstream data from major ISPs (however sketchy and frightening that is) are probably more reliable than Alexa's panel.