As someone who went to an "elite" institution, I wonder why all education can't be elite. In the past, there were physical limitations -- only so many students could fit in a lecture hall, on a campus etc. So the optimal arrangement at the time was to try to match the highest-potential students with the most qualified educators -- a system that could be gamed, requires imperfect approximations, but the best that was…
Elite isn't about the quality of the instruction. Elite is about who is instructed. By definition, you can't have a broad-based, democratic elite.
If you read the article, I think the author would disagree, as he refers to Yale and Columbia, not himself, as an elite education.
Here's a thought experiment. If Harvard's professors were swapped out for high school teachers, "elite" students would be less inclined to attend, and over several years, the quality of students at Harvard would almost certainly drop.
Conversely, if someone created a university with all the world's most renowned lecturers, in several years, "elite" students would likely be yearning to attend.
And I'm not clear on what you mean by "democratic elite." There would still be elite students. Two things would be different:
1) Their designation could be determined by cleaner data than was possible in a pre-MOOC world. In the current world, there are few clean baselines on which to evaluate students from different high schools, for example, which is one of the main reasons standardized tests like the SAT exist.
2) If we assume that a better lecturer will help increase a student's knowledge, regardless of the student's quality, then every student's knowledge could be maximized in the post-MOOC world, not just the small fraction that are able to gain entry to elite institutions.