Or would the fat of the hamburger blunt the insulin response of the white rice?
Fat lowers/slows the insulin response when eaten with carbs. If that's your goal, then those two are good to eat together.
However, if you want an insulin response, like say after a workout, then you probably would want to have a protein source that's low/no fat like whitefish or chicken/turkey breast.
I hate Gary Taubes for spawning these kinds of questions.
Bottom line, you'll be fine.
One of my favorites! I also use ground venison, shredded pork roast and chicken.
Adding white rice to my meals makes me get tubby. I do eat it once or twice a week because I love it, but I tend to overeat when I have the rice added in.
Using low lectin/nightshade free primal to control autoimmune arthritis. (And lost 50 lbs along the way )