If I buy a CD or download (legally) and they get their cut, then I can play the song. I paid them for thier intellectual rights. I can turn up my stereo and blast the neighborhood and the only law I break is local sound ordinance or not getting a permit for using a Public Address system. I can play it as background in a restaurant. I am not in violation of copywrite.
Now if somehow I make money from the public playing, say I am a wedding DJ, perhaps I am in violation.
Sorry for the long delay in responding. Had to go to work.
Holden, if you play any music that is copywritten thru BMI, ASCAP or SESAC in a public setting you owe royalties. About 15 years ago BMI went on a rampage and hit thousands of restaurants, bars, retail stores, grocery stores, ect. They gave the owners the option of paying yearly dues or being fined for back royalties. The courts backed the copywriters because under US law they are entitled royalties for any public performance of their product.
Just because you paid royalties when you bought the music does not mean you can play it anywhere you want. Those royalties only cover your personal, private use.
Here is a link to a good article on performance royalties thru BMI & ASCAP.
http://www.wooddonut.com/writing/essays/royalty-politics.html