Apple Music downloads saving to incorrect folder

The plot thickens!

If I turn off lossless quality and then download one of the files that was being placed in the Music folder, the .m4p file is then downloaded to the Apple Music folder. Mystifying.

I think this answers the question above regarding ownership. I do not, in fact, own this file. I did not purchase the file. But, Music.app thinks I purchased the Lossless version of it (when Lossless downloads are turned on).

I am going to guess that this is a bug, and I am also going to guess that this bug will never be fixed. So, the only way to separate my own files from the imposters is going to be to sort the folder by file-type.

I have discovered another interesting wrinkle. The files that are being incorrectly placed into the Music folder instead of the Apple Music folder are also showing up as Purchased in their file info.

I didn't "purchase" this file. I subscribe to Apple Music, and I simply added the album to my Library. I have tested this by adding tracks to my library, downloading them, and checking their location and purchase status. Anything marked as "purchased" is placed in the Music folder, while anything else is placed in the Apple Music folder. Maybe I'm confused about what "Add to Library" actually means? But I am not buying these albums (as one would buy a record in a brick-and-mortar shop). I only subscribe to Apple Music. Do I actually own these files? If I stop subscribing, can I still play them?