It’s tricky. I’ll talk about the general then the specific.
In general, your notion of "didn't get permission" doesn't really reflect how the music industry works.
Generally, a venue pays for a universal license to use recorded music. There are three major licensors: ASCAP, BMI and SESAC. If you get an ASCAP license, you can play any ASCAP music in your licensed venue without limit. I don't know if you have any records or CDs, but look carefully at the disc or the liner notes, and you'll see ASCAP or BMI next to each song. That tells you whether you can play it on your license.
Licenses go to the venue or application, not to the person. So for instance if you have a bar and grill, of course you get an ASCAP and/or BMI license, and that covers the bar's normal activities as agreed in the contract. If you then create a Youtube channel, you would need to negotiate a separate ASCAP license to use music there.
Each one is negotiated and priced separately, and you are negotiating with ASCAP, BMI and SESAC.
Keep in mind a blanket license for the venue, say a baseball park, is not enough, as they exclude political events specifically.
Political campaigns have to get the same blanket license as everyone else. But for political campaigns, particularly, ASCAP etc. provide an “opt-out”, by which an artist can exclude themselves from the license.
Of course the artist usually has failed to do this when they hear their music on coverage of the event. The artist still has some recourses in the area of false endorsement and a few other legal theories, but they’re complicated.
However a campaign will usually honor the artist's wishes. In theory, the artist’s legal options would take years winding through the courts, and the campaign would be long over by then. But in practice, the artist would likely team up with the opposition, and now the campaign is squared off against two different experts at using media - the other campaign, and the artist, who got where they are by playing the media well. The campaign doesn’t want to fight that fight, because a knock-down drag-out media palaver with a universally beloved musician is not a good look.
Now there is something called a "compulsory license", but that is about a performer's right to use a song someone else has written. (But they must still pay for the use; and ASCAP/BMI/SESAC handle that too). That would come up if the campaign's house band was playing Fleetwood Mac songs.