The following is the nutritional breakdown for a 3oz serving of tater tots. Potato Nutrition Facts and Health Benefits. The stir fry link you provided did not give an oil quantity, but according to the same site homemade hash browns Potato Nutrition Facts and Health Benefits do have a higher fat content that the tot. But the serving size given is for a cup of those hash browns. So while not the same as the Chinese recipe, I think it is a good indicator of just how much fat is potentially used in home cooking. When I cook, I always use 3/4 less to zero of the oil/fat that a recipe asks. And that is a benefit to scratch cooking. You control how much or little fat and salt go into your food. You do not need to plan around the levels provided by the food manufacturer.
I do wish the show would provide the nutritional analysis of the food the school was/is providing as well as Oliver’s food because there are a number of factors that lead to obesity aside from processing. I’d be curious to compare those to the Oliver plan.