As someone who has spent 20+ years hosting a radio program, played in bands, and ran a venue, I am pretty well-versed in a variety of music matters, especially when it comes to these kinds of complaints. I am not a lawyer (I know some of you are tho).
I think it is important to remember that this pertains to licensing and copyright in the US. Other countries have very different ways of handling things. Licensing and copyright issues are also not the same things.
The complaint largely revolves around copyright, but IMHO this falls under fair use on account of its transformative nature. That the original song is in the public domain isn't important here—it's this specific performance of the song, by these artists.
Interestingly, they list all their TV/film placements, which are handled by
sync licenses. Live music at sporting events fall under
blanket licenses, which are handled by the venue. NBC/Comcast pays for a similar license for TV/streaming. Anything that is composed for the network falls under a sync.
(In the US, royalties are paid out by the mechanical, not the performance. But that could change if the American Music Fairness Act, a bill currently in the House, gets passed.)
I dunno, these guys could have filed a good ol' DMCA complaint. But since they are so concerned about the "integrity of their professional reputation," they got their dad to file a lawsuit for them and create this embarrassing public spectacle for the sole purpose of settling out of court. I hope it gets tossed out because its so frivolous. Even more ridiculous when one considers both the plaintiffs and defendant reside in the LA area.
Look, I get it. The music biz is a pretty ****ing dire place to be at the moment. Royalties aren't coming in because streaming platforms pay abhorrent sums to artists (and are giving them to ****nuts like Joe Rogan instead). Venues are barely getting by, at least those not sucked up by AEG. Touring is a game of YKW whack-a-mole. Even the big names are cashing out their catalogs like pension funds. Musicians are basically betting that Bandcamp Fridays are going to dig them out of these holes when the real problems are structural.
I don't believe that artists should be pleased with the free PR of music in figure skating. They're right. But nickel and diming athletes in a sport where there's no money to be had is ridiculous.
I think at a certain point in your competitive career—especially skaters who are at the Olympics—should perhaps rethink their approach to securing music. It honestly would not hurt skaters in the US if they approached the matter similar to a sync license. That + blanket licenses would offer some security for both artist and athlete.
For all we know, it might actually improve the overall quality of the music we hear.