Sometimes the compound or hyphenated identity for Canadians and Americans isn't always one that is labelled by the person themselves, but sometimes by others.Precisely!
... which again is part of the issue with the mosaic, i.e. if you're a 'Chinese Canadian' you're a Canadian who uses a qualifying adjective whereas if you're an Italian-American you're a compound noun! The notion of 'Canadian' in this case is still fairly rigid, not evolving through the influence of our diversity.
For example, there are cases where some people have gotten some flak for actually rejecting a compound or hyphenated identity. One that comes to mind is when Raven-Symoné said that she didn't want to be labelled African-American, but just American, some people in the media actually criticized her for that.
I honestly think people should just chill out with the "identity policing". It's all right to be proud of one's own cultural, ethnic or racial heritage but telling others how they should or shouldn't identify is a bit silly.