Bizarre London "Terror Attack"

This story is quite confusing and gruesome, with some guy getting beheaded (?) in the street and the apparent killer with bloody hands, being interviewed before the cops came and killed him and his accomplice (?).  Because it was apparently some crazy Islamic dudes who did it, this is being called terrorism.  The whole thing sounds kind of fishy to me.  what's not clear is how the incident started-- was it provoked by the soldier saying something, or the attackers just went nuts?

NYTimes piece on this story, and the attack is causing a high level stir for some reason.

Gleen Greenwald weighs in on this too.