Apple's response is wrong. I've purchased ALL my iTunes content through the same account. Some show up as Purchased and some show up as Ineligible. When I view my movies as a list and select "View All", duplicate movies appear. And always, the downloaded one is Ineligible (and will not be visible in IOS) and the iCloud one is Purchased. Downloading the "Purchased" one does not fix anything. I have the same issue with TV Shows.
Apple, please fix this bug. And stop with the lame excuses (lies).