Is it actually true that doing sit ups and crunches every day will help burn stomach fat?

Not by themselves.: There is no such thing as spot fat loss. You would need to lose weight in general & a certain proportion of that will be abdominal fat. This can be done by eating healthfully, being physically active and making sure that calories burned exceed calories consumed. However you can improve your appearance by toning your abs. To tighten your abdominal muscles consider doing crunches, reverse crunches.