I think one distinction we should try to make is that a "public intellectual" is someone who actively seeks to relate academic/scholarly research and methods to the public in accessible, but not simplified, terms and is open to serious debate. A "thought leader" tends to be associated with little scholarly rigour, a tendency to skirt debate, and over-simplification of complex ideas.
I think the author did have a good distinction as well. A "public intellectual" questions and interrogates, while a "thought leader" seems to inordinately promote and prophesize. (I'm thinking of someone like Ray Kurzweil as a "thought leader" here) That's not perfect, but it seems to serve pretty well.