As it turns out, "anonymous password authentication" means that it gives you a randomly generated string which you have to copy and paste into another box each time you submit a comment. It sounds like something a machine could do because it is something a machine could do with ease. And yet nobody seems to have noticed this for two reasons:
1) The author deletes all the comments on his blog questioning why the system works
2) It has a 4.5 star rating on the WordPress plugin DB
As a result, the author is still making ridiculously exaggerated claims about the capability of his system, like "If Gawker had been using the anonymous password authentication built into Spam Free WordPress this incident [the Gawker break-in in 2010] would not have happened." Another gem is "CAPTCHA is not used because it is hard to read, unnecessary, easily cracked, and reduces the number of real comments substantially."
So there it is, another snake-oil salesman spreading FUD and making users (of some very popular websites[1]) suffer.
[0]: http://www.toddlahman.com/spam-free-wordpress/ [1]: http://www.raspberrypi.org/