Mr. Cutts indicates in the video that it doesn't matter if the site is .edu or .gov, but it's the value of the site that matters. [He even references PageRank, another blast from the past.] That makes sense to me, but don't those sites inherently have more value?

But, I would also argue that a link from a .edu site to a automobile tire company would not have the same weight as a link from that same .edu site to a text book publisher. A link between a school and text book should carry more value due to the relevancy of the link, versus the tire company where there is little relevancy.