You can hide music from your library. Apple put out a support page on how to do exactly that something like a week after the U2 debacle.

Here's how to delete from iCloud Music Library: https://support.apple.com/en-us/HT201323

Here's how to delete iTunes Store content: https://support.apple.com/kb/HT204343

For the latter, it says that deleting something you haven't downloaded will hide it from your purchase history as well.

Well you imported those Starbucks songs yourself so you can't really blame Apple for that. Try the "Delete from Library" option -- it works great.

Perhaps but I never explicitly requested or copied that music to my phone, yet it appears there anyway.