My wife has tried and failed on many occasions to get a Hertz
rental car [ other hire companies have the exact same policy] from several airports in the UK and France, without her own credit card. They won't take my Amex, her debit, online, nor cash [ "Sorry we stopped taking cash after an armed robbery here
." ], checks, gold bars - it must
be a valid credit card, in the name of the hirer, presented at the desk at the time of hiring by the named driver. Reason? Fraud. And don't get me started on their scams for damage waivers, second driver insurance, road-tax levy etc. which virtually double their online quotes....
I guess if you say it's your US law, but a third party would never get to be responsible for a first parties debt in the EU just because the hirer is working in their home. Sounds kinda unconstitutional to me.