Foreign owners in the EPL have certainly contributed to the record transfer fees, but I don't think it's necessarily specific to American owners or even to English clubs.
While Arsenal, Liverpool, and Man Utd are all owned by Americans, I believe Roman Abramovich (Russia) of Chelsea was the first foreign owner to really start splashing the cash when he bought the club in 2003. Of course, Chelsea are still among the top spenders, but Man City (Emirati owners) have currently spent more money on transfers than any other English club over the past 10 years.
Over in France, Paris Saint Germain have had Qatari owners for about ten years now. They've never been afraid to pull out their check book, and the two most expensive signings at the moment, Mbappe and Neymars, are theirs. Over in Italy, two of the three big spenders have had foreign owners, with AC Milan now being owned by an American investment firm after their Chinese owners defaulted on their debt, and Inter Milan having Chinese owners. Though before the Americans and the Chinese, AC Milan had a lot of success and spent a lot of money under Italian owner and prime minister Silvio Berlusconi.
Not all the big spending clubs have foreign owners. For example, technically Barcelona and Real Madrid are owned by the fans, who vote to elect a club president every so many years. One reason Florentino Perez is famous is that as president of Real Madrid he's never seen a transfer record he didn't like, even 20 years ago. He managed to sign Luis Figo from Barcelona when he was first elected in 2000, which was only slightly less insane than if Real Madrid had managed to buy Messi from Barcelona in his prime, and that also started the 'galacticos' era where Perez bought at least one world class player for a world class price almost every season.
Going back to Italy, the third of the three big spenders is Juventus, and they have been owned for almost 100 years now by the Agnelli family, the same ones that founded the car manufacturer Fiat.