My mom's childhood friend who was a Holocaust refugee has no reason to lie to me (about not being able to go to any other country they tried to escape to), I think. But here, I pulled up some sources to placate you guys:

https://en.wikipedia.org/wiki/Shanghai_Jewish_Refugees_Museu...

https://en.wikipedia.org/wiki/History_of_the_Jews_in_China

http://www.ushmm.org/wlc/en/article.php?ModuleId=10007091