Mr. Speaker, we have been having troop exchanges with our allies, be they British or American, for decades. It is completely normal for soldiers of one country to remain under the command of another in such circumstances. However, their own country, Canada in this instance, reserves the right to order its soldiers home, should it so choose. Since these are good allies and the soldiers are not in a direct combat role, Canada has decided to leave them where they are.
In the House of Commons on March 20th, 2003. See this statement in context.