There are few ways to verify their claims. Find out how many copies are printed The printers invoice will tell you this. You do not really need the Canada Post invoices. Ask, they should be able to tell you. It is only partly true.
Printers do provide inexpensive mailings to their clients.
However, they only send mail where they are told to do so. They are in the printing business not the media. At this point you will have to rely on their documents. As long as you have the printers invoice you are ok. It is up you to make the disclosure of this information a condition.