Insulin is not required for fat storage. Insulin spikes do not create energy out of nowhere and don't suddenly make the same number of input calories multiply. Also, insulin spikes are nearly unpredictable anyway. Carbs aren't necessarily the trigger, protein and fat can be too. Sometimes foods are synergistic and spike insulin together more than eaten separately. Insulin spikiness is also determined by food in your stomach, further complicating things. For example, having fiber with a meal can "smooth out" an insulin spike.
I summarized some articles that dispel insulin voodoo here, if you're interested: https://www.reddit.com/r/Fitness/comments/j853z/insulin_an_u...