Not true. Traditional radio stations do pay royalties.

"For years, stations have paid royalties to composers and publishers when they played their songs. But they enjoy a federal exemption when paying the performers and record labels because, they argue, the airplay sells music."

http://articles.latimes.com/2007/may/21/business/fi-radio21

Well, that's interesting to know. That's certainly not how it works in Australia, which coloured my perception of things.

They pay royalties to song-writers but not performers.