Yes. And an Englishman can tell that an Australian of Franco-Italian descent (Toni Collette) isn't actually an Englishwoman when she plays Harriet Smith in Emma.
Yet I don't recall any press furor over that movie.
The Japanese are simply more xenophobic as a society than other cultures are.
They need to deal with that cultural limitation - it isn't Hollywood's responsibility to pander to it.
Last year there was a Japanese TV series about the brother of Pu Yi who married a Japanese princess as his wife on Hong Kong's TVB. The character of Pu Yi and a couple of others were played by Japanese actors/actresses. The results were lots of disgust from HK Chinese: "How could they have Japanese playing Chinese?" etc.
The prejudice runs both ways. Most mainland Chinese TV series about the Sino-Japanese war period have Chinese actors/actresses playing Japanese characters and nary a word of protest is sounded in China.