Why are the songs on the iPhone, but they aren’t downloaded

After trying a series of troubleshooting moves, including restoring my iPhone from an iCloud backup, the only thing that worked was restoring my iPhone from an iTunes backup, as described in this article.

See if this works for you... but this will remove ALL OF YOUR MUSIC FROM YOUR PHONE. So, I hope you have it somewhere else before doing these steps.

• Uncheck "Sync Music" in iTunes on the Music tab for your iPhone.
• Check "Manually manage music and videos" in iTunes on the Summary tab for your iPhone.
• Go to the Music on the left tree under your iPhone in iTunes.
• Select all of the music (CMD-A) and delete all of the songs.
• Go back to the Summary Tab and click Sync.
• At this point, your iPhone will have no music on it and will report that correctly.

This worked for my iPhone that was stuck in some weird limbo with Match. I was able to turn back on Sync Music and do the albums I wanted. Now my iPhone's Usage count matches iTunes.