I think that Apple adds DRM to some files that you buy from iTunes but not others, so the files that appear as Protected AAC will never play, while the files that appear as Purchased AAC might play and might not. Does that match what you're seeing?
In iTunes, you should be able to convert the DRM files to unprotected MP3 or AAC files and attach those versions to your songs. It is weird that Apple doesn't allow third-party apps full access to DRM files, but allows you to make a DRM-free copy of those files in iTunes.