Triac Turn-on Stress Calculation
There sure is something wrong with your reasoning. With 120Vac, the peak voltage across the snubber network will be 120V x 1.414: 169.68V. this gives you a peak current of 3.6A. (The app note you linked to starts from 230Vac. Peak voltage: 325V.) Now you have to calculate the rise time but I think it's better to measure it after you build a proto-type. But you can make a guess on where to start based on the calculations you did. 

It's difficult to see the current rise time in the app. note you linked to. It looks like 25A/µS to me. You should also take into consideration that the peak voltage appearing across the triac might become higher if you're switching an inductive load like a motor for example.