The New York Times on the Kindle (which is what I read) has headlines that are pretty clear - just like in the newspaper. For instance, "Iran's op Leader Dashes Hopes for a Compromise" turns out to be Iran's top leader not wanting to compromise.
And the preview in the articles List view shows the first two lines of the story (at least with the font that I have installed). Sure it would be nice to have a little more, but I can generally get a sense of what the story is about and whether I want to read it. If I can't tell for sure, it takes about .5 seconds to look at the article, then skim it, and .5 seconds to go back to the main menu. Not really a big deal.
I get what he's saying, I just think he's overstating it. And I think he doesn't give enough credit for the things that the Kindle does better. For instance I can skim all 15 of the headlines in the National section much faster than I can flip through the pages of the front page section of the Times. It's much more efficient, in my opinion, which is why I can say I read more deeply in the same amount of time.