If you look at the Lew Rockwell homepage you will see that they have an Alexa referral box on it. The Alexa rating system works only for Browsers with the Alexa Toolbar installed. The Alexa spyware collects surfing data on those browsers with the toolbar installed. Currently the Toolbar only works with Microsoft Internet Explorer.
Lew Rockwell hypes the Alexa Rating by featuring it on his hompage and often mentioning his ratings as the example you have linked. His users are more likely to use the Tool Bar offered by Alexa if for no other reason than they are aware it exists, which would not be typically true of the other sites he shows in the comparisons he listed.
Alexa ratings my be relevant comparisons for sites that do not make prominant reference to Alexa and thereby Skew the ratings upward. Also, I don't think he is doing his readers any favors by leading them to a toolbar that loads spyware on their computers.
According to the Alexa "Technology" page the traffic ratings are based on snapshots they take while web-crawling:
"Alexa is continually crawling all publicly available web sites to create a series of snapshots of the Web.I don't see any indication the toolbar is used for gathering traffic ranking statistics, and it seems unlikely since you don't need a toolbar to web-crawl (what Google and others do)....
By analyzing the data we receive from our updated snapshots of the Web, we can tell our users how their traffic ranks in comparison to other web sites and how many other sites link to that site."
Do you have information from somewhere else that contradicts this?