I think there might be a little bit of confusion here, as two issues are being discussed at the same time.
First, when you join the Forces you're offered a job in a particular trade. You can accept the offer if you like that trade, or decline it if you don't. So there's no question of getting into the Forces and THEN being sent to a trade you don't want.
As others have said, some trades are specific to one element, e.g. all infanteers are in the army, and all boatswains are in the navy. Some trades exist in two or three elements, e.g. RMS clerk or supply technician. In those trades you can end up in any posting regardless of what uniform you wear, e.g. you can find army clerks in ships and navy supply technicians at air force bases.
Finally, some trades have element-specific sub-trades, e.g. logistics officers. A naval logistics officer has taken training specific to the naval element, and presumably will spend most of his time working in that element, but if I'm not mistaken, can still be posted to a base or other employment in another element. (Getting slightly outside of my experience on that issue, so better information than mine should be sought.)
But in all cases, a person really joins the Canadian Forces rather than the navy, army, or air force as such. Anyone in the Forces can be sent anywhere he's needed, inside or outside of his own element (e.g. to teach a course or fill a position that doesn't have a specific trade requirement).