I too use my CAA card to get AAA rates up here all the time. Quite often you can't get CAA rates in Canada (go figure) as they only offer the AAA.

Book it and don't even worry about it. Think of it this way. How often do you even get asked for your AAA card when booking those rates? I think I have been asked maybe 3 times in 2 years (over 200 nights). Worst comes to worst you can just argue (politely) that they are both Automobile Association cards