Per the point you were making in your essay, though, he does this because most of his students are post-docs and (1) they understand what a "fellowship" is and (2) do not necessarily want to be a "student" again. To a postdoc, especially, student implies having to pay for it.
The other folks upthread are sort of missing the point, honestly, because when it comes to a word like "student," it touches on issues of identity and association. When someone (e.g., a friend) asks your students, "What are you doing?" they're going to respond with, "Oh, I'm an X at Hacker School."
You want X to be something the students feel comfortable saying to friends, families, and co-workers. Whether "fellow" is too pretentious or not depends on who your students are and who they'll be saying "I'm an X" to.
Thank you for taking the time to make such a thoughtful and considerate comment. You have gotten to the nut of what I was thinking when I wrote the post and said it more eloquently than I did.
As a side observation, I think you can actually make "fellow" in particular a bit more cool/casual, especially since it is a rather ambiguous term anyway and there are many kinds of fellows working on many levels out there. All it reliably seems to connote a learning environment, some degree of selectivity in participation, and less structure than a traditional school program.