I suspect that the threat of something similar to Global Magnitsky Sanctions (cutting them off from all dollar-denominated accounts everywhere) is a pretty big stick to use in negotiations. For a financial firm like Binance, access to bank accounts that can send dollars to and from US firms is pretty important, even without any US customers at all (losing access to banking in France, Cyprus, etc. would be equally difficult for them).

The US has recently (gradually over the past 20 years or so) started to really weaponize access to dollar-denominated accounts, essentially conscripting all the banks that want to do business with American banks into service of American foreign policy goals. This started in the aftermath of September 11th, for terrorism, then spread with the Magnitsky act of 2012 to include international corruption, and has slowly spread to more and more areas. So far the US has been somewhat judicious about using the tool- they seem to be aware that if they use it too often people will eventually just build ways around it- but it is a pretty big threat to wield against a company that absolutely needs to do business with somebody's banks.