You're on the right track, Dawn. 'Have to' and 'Should' are debatable. If you are challenged by CWS to prove something's status, you 'should' have the paperwork. Otherwise, you could end up in court. If I was buying an animal that I thought could be a problem, I would 'have to' have the paperwork in most cases.
However, keep in mind that CWS is generally only concerned with CITES App. I species which are rarely involved in the herp hobby in Canada, with notable exceptions. They are not out checking paperwork on green iguanas and boa constrictors (App. II).