Update: As noted by Harry McCracken over at Technologizer, it has actually been Apple's longstanding policy to forbid in-app purchases -- the Kindle and Nook apps send you to a browser -- so Sony's desire to do so will have been the major cause for the Reader application's rejection. That doesn't invalidate the second concern expressed in the New York Times article, that Apple will no longer tolerate content brought in from external stores, which is a displeasing development, if true.
Update 2: Looks like McCracken nailed it -- Apple's come out with a statement pointing out that the App Store guidelines require that apps that allow content purchases must also allow them in-app through Apple's official iTunes-backed system. We can't imagine that Sony is thrilled with the idea of cutting Apple in on Reader content, but if they want to play ball, they should be able to score an approval. Notably, Apple says that they are "now requiring" this even though the guidelines haven't changed, suggesting they're just now getting around to enforcing it; the effect on iOS' Kindle and Nook apps isn't yet known, but we wouldn't be surprised if Apple started nudging them in the direction of pushing updates. More on this situation as we have it.