This is true, and still true to some extent once you compensate you can't compare the two numbers. There are large costs associated with living in the US like health insurance that just don't exist in the UK where I live.
Paying a given salary in Germany is a lot more expensive for a company than paying the exact same salary in America. There are both more taxes on the employer side and more labor regulations that cost money to comply with. The number of hours worked tends to be different, too.
Of course there might be exceptions, but isn’t it reasonable to expect that companies in bigger cities have more business and can therefore pay more?
That would only really make sense for the location of the sales office, I guess?
Where you put your developers shouldn't make much of a difference to how much business you have?
However you are up to something: big cities tend to be more productive. That's the reason people and businesses put up with the higher rents and other inconveniences. See https://en.wikipedia.org/wiki/Economies_of_agglomeration
Perhaps the company doesn't see it worthwhile to argue over peanuts.