As the article mentions, a lot of the rankings seem to be influenced by the popularity of the service. Twitter and Facebook are going to have more complaints simply due to the fact that more people use them.

Twitter in particular has a very good API, I have never used Digg's, LinkedIn's, or Paypal's, but I doubt very much they are better documented and easier to use than Twitter's. (I have had some problems with Facebook's API, so perhaps it is deserving of its title.)

A better way to run this survey would be to only allow people who have actually used all the API's to vote. It would be difficult in my opinion to vote for an API as the worst with no basis of comparison.