Giving this some thought, I think the reason Apple says don't talk about file folders is because they think file folders are a poor way to organize files and, after even more thought, I am inclined to agree.Now, the reason the "All Songs (grouped by folder)" list is hidden on the iPad is because Apple's guidance is to de-emphasize the file system. You're not supposed to talk about folders in your app. Though I suspect when you start talking about cloud storage, they have to make some concessions.
Folders only provide one, fixed organization of the files they contain. That organization is entirely at the mercy of whoever is putting the files into folders. (Now that I think about it, this is a problem with real, paper file folders too.)
Now consider iTunes. People have massive libraries of songs. iTunes does not give you a flat list of songs. Quite the reverse. iTunes allows you to sort, select, filter, and classify that library up the wazoo. But it is all done by having tags in the metadata for each song and then sorting and selecting according to the metadata.
I think the right answer for Synthesia is to provide metadata tagging of the MIDI files and views of the library based on the metadata. Synthesia should probably be metafile-centric. Part of the metadata is the name and location of the MIDI or MusicXML file associated with the song described by the metadata. Neither file names nor file folders should be directly apparent to the user.
Ditch the organization by file folders. Apple is right. It is an inferior solution.