First, do NOT believe anything printed in a "List Of Towing Laws" on the internet. EVERY such list I have ever seen is WRONG in many ways! You have to do the research, and find the actual law for yourself.
Second, Reciprocity ONLY applies to registration, driver licensing, and insurance. Even then, not always. For instance, even though my Kawasaki ATV is licensed and street legal as a Low Speed Vehicle here in Montana, that does not mean that other states will allow me to ride it on the public roads, and, as already noted, just because I can tow bumper-pull doubles (Travel Trailer/boat or ATV trailer; 75 foot maximum length) here does not mean that I can do so in other states.