There appears to be some details missing from this story. The only reason they would have charged you was because you were having the service department test a battery while in the car. The battery tester at the auto parts desk has a machine to test the battery but you need to bring in the battery. It is clearly stated in the warranty that all batteries are pro-rated after there free replacement warranty has expired. This is as far as I know, GLOBAL. It does not matter where or WHO you buy an auto battery from, auto batteries are now pro-rated by the manufacturer. It is also clearly stated that installation is not included.
Unless merchandise, auto batteries vendors are very strict when it comes to warranting them and issuing credit to companies that sell their batteries. In fact if you make one mistake on the battery warranty papers while doing the exchange, Canadian Tire will entirely lose the credit. Auto battery warranties have NOTHING to do with Canadian Tire. If you have a complaint as to why they are pro-rated, talk to the manufacturers of today's auto batteries, exile, interstate, etc
In regards to using CAA, CAA is a MEMBERSHIP you pay for. The battery service is part of the membership.