Purchased music keeps appearing (iPhone 5, iOS 7.1)

I have downloaded music directly from iTunes onto my iPhone from the app. The problem is some of the songs I don't want on my iPhone and I just do not have the space for it, and I would like to add different music to my iPhone. The problem is I have "show all music" unchecked, I also have "automatically download music" unchecked, as well as pretty much every answer that has been given online to resolve this problem. I don't use iCloud or iTunes match.

I even closed the music by going to general > usage > music and deleting all of the data. That still didn't work. I even factory reset my phone, and once I sync my phone the purchased music will completely sync back onto my phone. I know it is only the purchased music, but seeing as I only have a 16GB iPhone, I absolutely NEED more space, and it is killing me that the only way to get rid of it is to manually delete each of the 500 individual songs by swiping left on the iPhone.

If anyone can help me I would really really appreciate it. I've spent countless hours being frustrated by my phone trying to get this music off in order to have space to add new music.

Any songs I had in a playlist called "purchased" kept reappearing (Even after I deleted all music from the usage setting). Once I deleted that playlist they did not.