Reciprocity of drivers licenses means that if you are legal to drive in your home state or province, you are legal to drive anywhere in North America. You do not have to follow another state's licensing rules so you don't need a CDL, a non-CDL Class A,etc, unless you need it for your home state. In most of Canada, for example, there is no concept of a CDL, there are just driver's licenses for classes of vehicles (Ontario does have a restricted Class A for fifth wheels under a certain weight limit, still not for RV's only or commercial or non-commercial.
What is not reciprocal is the vehicle. It must conform to the laws of the state. This applies to triple-towing, axle weight restrictions, if GVWR matters or not, over-all length, and so on.
Brian