Yeah... that's even worse... All new recruits have to swear to the Queen too, and she is the Command in Chief of armed forces. But to be fair she delegates most of the power to the General Governor of Canada which is appointed by the recommendation of the Prime Minister which is indirectly elected by the citizens.

Balance of Power in Canada is very tricky and obfuscated, but here is a fairly accurate (and fun to watch) explanation by Rick Mercer :

https://www.youtube.com/watch?v=yi1yhp-_x7A