This is how it should have worked:
1) Apple Music for all the stations, curated playlists, social connects, and anything you don't have but want to listen to. This actually works as its suppose to from what I'm seeing other than some "add to playlists" and "love" bugs.
2) iCloud Music Library = My Library which simply adds to AM without touching the way its set up. How files are named, where they are locally, artwork, other meta tags are left untouched. This should work like iTunes Match frankly. Whatever iTunes doesn't have simply gets uploaded.
3) Any available song from AM or IML can be added to a playlists or loved. This should be seemless.
4) Searching for a song/artist/album should first give results to let users know which item belongs to who, an icon should be displayed next to the song title: The Apple logo should be used if it's an AM track, or the Profile icon if it's yours. For example, The Beatles or Prince should have the Profile icon to let me know that it's my track. We can even make more simple by assuming all songs are AM's unless there's the Profile icon.
5) Anything downloaded to your make from AM for offline use should be put in a separate folder in the Finder for iTunes. That way users don't accidentally delete something they own because it's mixed in with your media files. Users should know anything in this folder is DRM'd to the gills. Call the folder Apple Music Protected Downloads or something.
6) Any downloads that come from a users library should remain DRM free, just like iTunes Match, yet put in a separate folder (your regular iTunes Media folder IF it's not already there), away from AM.
7) For iTunes, there should be tabs for "My Music", "Apple Music", and "All Music", depending on what view you want to see. Simply throwing everything into one is a recipe for disaster and alot of pissed off users. Especially when I see that you've replaced and renamed my tracks and they are now DRM'd. Makes me think there's a conspiracy going on. There's no reason for you to be replacing my stuff with yours.
The integration should have been seemless. My personal collection should have NEVER been touched. All Apple had to do is say, "ok, this folder is User X and this folder is "Apple Music, however we'll make it seemless so users don't have to worry about which is which.