Do Canadians care about this?

The vast majority of people throughout the world see Elizabeth, Charles/Camilla, Will/Kate, etc. as being completely and utterly nothing but British royals (my source on this is much world travel, living outside the UK for many years, reading of the international press, etc.). This means that when people see Elizabeth on Canadian money, postage, etc., they are confused as to why Canada is not independent of Britain. Do Canadians even care that they are perceived as not being independent of British rule because their head of state is a queen that the rest of the world views solely as being British (she is most often casually referred to throughout the world as the queen of England, even though I know this is not her official title). Is this a PR debacle for Canada? It must be noted that responses from many of those who are top contributors to the Royalty section can not be taken as a good sampling for this particular question. A majority of these top contributors are monarchists as evident by the amount of time they spend defending monarchy on this site (i.e. Ms. Minerva, Dart, capitalg, etc.). I hope to get responses from everyday Canadians who have a wider range of viewpoints. No disrespect is meant to people like "capitalg" because he is always quite civil in his responses. It's just that his stance, and that of Ms. Minerva, Dart, etc., is already so clear in absolute support and adulation of the monarchy. Thank you.