I'm actually quite surprised by that. Those are both excellent schools with top notch math departments, and the example that he mentioned in the article (about not really grokking the second order ODE and what it meant re: the phase space plot, etc.) indicates that he took a seriously badly taught class. I'm kind of surprised you could get through a diff eq's course at either school without having such basic stuff taught to you...makes me wonder who the teacher was, maybe it was pawned off on a grad student?
Edit: whoops...just looked back at the article, turns out he didn't take that diff eq course at Caltech or Berkeley, it was at a local college. That explains a lot. I'm not going to say that there are no good teachers at mediocre schools, nor that there are no bad teachers at the good ones, but on average there's a huge discrepancy in the quality of the classes.
I had similar experiences, where I took classes at a local college while in high school, and thought I was stupid or something when I didn't "get" them, only to find that when I took them again at a better school they were, in fact, very easy topics.
I blame the textbook writers in part: for one example, Serge Lang's math books are extremely difficult as a rule, and leave a lot of the scaffolding out. Scaffolding which, when he taught classes himself, he always filled in to make for an amazingly smooth and effortless learning experience, but which lesser teachers would never think to talk about (perhaps because they don't understand it themselves, or at least don't understand how important it is to explain). It's really a shame that even now, after so many centuries of teaching math to people, the effectiveness of the process is still so utterly dependent on the teacher. Hopefully things like the Khan Academy will begin to rectify these problems.
Maybe it's not a shame. Maybe it's just an indication that teaching is hard, like art, science, programming, and discovering new theorems, not easy like answering phones in a call center or being a short-order cook.