Twisted, I do not know that paricular story, but it could well be true.
The Germans announced their intentions by the late 1930’s, however no one took them seriously. By 1940 Auschwitz hadn’t been built yet, In fact the entire “final solution” was only introduced at the beggining of 1941. Please remember, even yidden in occupied Hungary failed to beleive the stories they heard until it was too late for most of them.
Nonetheless there is no question that both Britain and the US could have done a lot more duringthe war, both in terms of immigration, and in terms of ruining the german plans.