Why data for Alexa does not show up (Score 1)

I am guessing Alexa does not show data for its own site because the toolbar posts there. Also, Alexa chart images in other sites might skew. The traffic would be almost 100% toolbar data posts, chart requests, and relatively little actual site browsing.

Yes they could be clever and filter that stuff out. As I said it is just a guess. Good a reason as any.