From the licensing company:
"Is it legal to play purchased iTunes music on my iPod/iPad/iPhone, CDs, MP3s or digital files for background music?
It is common in our digital age to be confused as to
whether we own our digital content.
When you pay to download music or even movies for that matter, you are essentially purchasing a license; you are leasing the content. Furthermore, you may only play this music in a non-commercial setting. You can listen to the songs to yourself as much as you like, but it is illegal to play in public.
Playing the downloaded music in your business, however, would violate copyright law because the act is now considered a public performance. Public performances require a Public Performance License (PPL) from performing rights organizations (PROs)."
If you could just play whatever you wanted, it would be IMPOSSIBLE to track royalties for the artists/songwriters/publishers, which is the sole purpose of ASCAP & BMI.