Turns out, the copyright issue is a complicated, but settled, issue:
> But the basic rule is simple: Standard licensing fees paid by broadcasters cover these uses, and the money makes its way, eventually, to songwriters as royalties.
Most of the time, when songs are included on television, producers have to pay for a so-called synchronization license from music publishers. Negotiations can lead to high fees for the most in-demand pieces, like Beatles songs.
But since the Olympics are considered a “live event,” even when tape-delayed, no such special permission is needed, said Steve Winogradsky, a lawyer who is an expert in music licensing. [0]
[0]https://www.nytimes.com/2018/02/14/arts/music/olympics-figur...