No - the United States does not pay public performance royalties to performers and sound recording owners when their music is publicly broadcasted on US terrestrial radio, nor do they pay Neighboring Rights Royalties to non-US artists whose recordings are played on US Terrestrial radio. Thus, other countries have also decided against paying US artists when their music is played on terrestrial radio in their own territories. This may seem unfair, but in reality it makes sense.
Consider the following example: You are US-based performer/recording artist who has recorded and released your music in the USA. This song then gets played on terrestrial radio, for instance, in the UK. You are owed Neighboring Rights Royalties, but you won't be getting any. Why? Because, think about the situation reserved - a UK-based artist records and releases a song in the UK which then goes on to get a lot of radio play in the USA (for example, the Beatles). The USA will not pay this artist Neighboring Rights Royalties. So in return, other countries refuse to pay US-based artists whose songs are broadcasted in their home territory. The line of thought essentially is, "why should we pay your (American) artists if you don't pay ours?"