Yep, I also agree. "Free music" apps typically scan a number of servers on the web for uploaded content from users, which can include songs, and then download that content. Copyrighted songs can be saved to the cloud by a user for personal use, but it's illegal to share the song to anyone else. The app developer can claim not to have any responsibility, since they're not the ones who uploaded the song, and they try to get around the legal issues by claiming that their app is for "research" only. I've seen fine print with those apps that say that the app user must delete the downloaded files from their phones as soon as their "research" is complete.
Apart from songs that artists purposely make free (or are intentionally on sale for free), the only truly free music you can download legally is public domain music (like Happy Birthday)(which interestingly was NOT public domain until only recently).
Bottom line: Pay for your music.