We all live in the same world and in an increasingly globalized economy and society. Products consummed in America, Europe, Japan or Australia are basically the same from food and clothes to music and movies (well, at least one can buy imported products from almost anywhere). The media keep us inform or problems, events and new trends all around the world, and therefore the argument that we do not belong to another country's culture is rather old-fashioned.
Alright, 200 years ago, an Englishman coming to Japan would have had almost nothing in common with the locals, from the way of dressing, haircut, food, customs, language, religion, etc. Nowadays, most Westerners and Japanese alike don't care about religion much (Americans are a case apart), wear similar clothes, listen to similar music, study the same subjects at school (maths, sciences, as opposed to Chinese classics and confucianism vs Latin/Greek in the past), and most people can speak at least some English almost anywhere in the developed world.
It's easier now with airplannes to travel to any other country, and more flexile visa requirements have recently facilitated the exchange of students between universities or people who want to live and work abroad.
As a result, I really don't think there is much difference in criticising another country (especially the government) than one's own country. Europeans have always compared, criticised and copied each others, and from a European point of view, there is little difference doing the same with the US, Australia or Japan.
My opinion is that people should care as much, if not more, about what happens in the country where they live than their "home country", if that happens to be a different one.