Not strictly true. An artist can refuse to license their work to a given station. That never happens in practice, but politicians being refused use of music has happened.

So, true in practicality.

> An artist can refuse to license their work to a given station.

Via what means?

First, radio stations in the USA aren't required to pay royalties to a recording artist, only to the songwriter via a Performing Rights Organization (PRO) like ASCAP or BMI. It follows that recording artists don't even have a say in whether their recordings can be played on the radio.

Second, songwriters don't have any control over public performance once they've licensed their work to the PRO. It's all or nothing. Songwriters can withdraw their works from the PRO, but then they have to negotiate with public performers through some other means. Radio stations don't have the means to enter separate negotiations with every songwriter, so they'll likely forego it, which practically means no airplay for artists who haven't submitted to the PROs.

> politicians being refused use of music has happened

That's not radio, and different license terms apply for campaign events. See https://www.congress.gov/crs-product/IF12775 for the details.