There's more. A friend on Twitter tipped me to this 4 month old post on a public forum, and the story is much the same. The ebook app had text, background music, and sound effects, but that wasn't enough for Apple. Also, a second dev chimed in about a month later on that thread; he had the same experience.
I also have a 4th case, and this one from the Baker Framework community. (BF is a pre-written library of code that helps you build ebook apps for the iPad.) One dev reported that his app was rejected because it wasn't app enough. Apple told him to submit it to iBooks, even though it's not clear that you could translate the design of his app into Epub.
On the other hand, the devs who maintain the Baker Framework have heard back from a bunch of developers who succeeded in getting their app into iTunes, which suggests that the rejected apps might be a minority. It looks like approval depends on who reviews the app.
So here's the problem, folks. Most of these apps have complex formatting that doesn't work well in iBooks. That's why they were submitted as apps.
Even if they do work, I wouldn't want to have them as ebooks. iBooks forces you to experience a number of faux-book effects that I really don't like. It inserts a fake crease down the middle of the screen and as for the fake page turn - ugh!
P.S. Apple does have a rule for this, but it's not being applied consistently.
* 2.21: Apps that are simply a song or movie should be submitted to the iTunes store. Apps that are simply a book should be submitted to the iBookstore"
What is a book?
P.P.S. If you have heard of other ebook apps being rejected, please let me know.