But it's often not all that arbitrary- it's generally pretty clear cut. You seem to think that based purely on the fact that the American, British and Canadian film industries are heavily intergrated. But outside the Anglo-Saxon world, this is in fact unusual- Bollywood films, most Chinese and Japanese films, Russian films, German films, French films, etc., normally have little if any American involvement. Many of these will be produced by companies from these countries, directed by people from these countries, largely set in these countries, predominately starring actors from these countries, funded by companies from these countries, and so to deny these being Indian or Chinese or French films would be silly. It is a useful way to label/distinguish films.
Some films might be considered to be a joint venture between countries- quite a few films considered to be American-Australian films, for example. Recently there have been more American-Chinese films- The Great Wall, for example, funded and produced by a mix of Chinese and American companies and starring a mix of Chinese and American actors. Trends of globalization might mean that increasingly fewer films will have clear nationalities. But, as we are right now, merging of the global film industry hasn't gone as far as you seem to think, and different countries have very distinct film industries, and so labeling these based on their countries does make sense. If I'm watching a film that is by any reasonable definition a Russian film, I might as well call it a Russian film.
Edit: Anyway, we should stop debating this so as not to derail the thread