How are rounded corners on rects harder than circles and ovals?
Is a rounded rect not just a circle sliced with straight lines between the quarter circles?
I get the feeling that what you mention is the precise realisation that Atkinson had when he figured out a way to draw them quickly. It's quite possible that he was initially thinking of ways to describe rounded rects using a single equation. Even one as undeniably brilliant as Atkinson can get stuck in thinking and overcomplicate things. A good night's sleep can bring a fresh perspective and make simplicity much more apparent.
I think he came to this realization while looking at all the examples jobs was showing him, which is why he suddenly agreed to give it a try.