Liberty actually does own the sport. The FIA is the governing body.
www.libertymedia.com
"The Formula One Group consists of our wholly-owned subsidiaries Formula 1®, MotoGP™, Quint and other minority investments.
The Series A and Series C Liberty Formula One common stock trade on the Nasdaq Global Select Market under the stock symbols FWONA and FWONK, respectively. The Series B Liberty Formula One common stock is quoted on the OTC Markets under the symbol FWONB."
en.wikipedia.org
"Liberty Media Corporation (commonly referred to as Liberty Media or just Liberty) is an American mass media company founded by John C. Malone in 1991. The company has three divisions, reflecting its ownership stakes in the Formula One Group, Sirius XM, and Live Nation Entertainment. The Sirius XM Holdings segment operates two audio entertainment companies, Sirius XM and Pandora. Sirius XM offers channels and information and entertainment services. Pandora is a streaming platform for searching for music and podcasts. As of 2025, Liberty Media owned three global motorsport businesses in the form of Formula One,[6] MotoGP and World Superbikes."