There are probably as many different opinions about that question as there are people giving answers to it. Especially with the more international production companies since about the 1970s.
I think my answer to the question would have to be "It's often impossible to attribute just one country to the production of a film. But does it matter?"
In the case of Dr Zhivago, yes it was an American production company that financed it (MGM).
Think about who goes up to collect the statue if it wins "Best Picture". It's usually the producer, not the director. In this case it was Carlo Ponti who would have collected it had it won.