You're close, but it's where those calories come from rather than the calories themselves that matter in this case.
This article explains my point better than I ever could:
http://eatingacademy.com/nutrition/do-calories-matter
Ultimately, the mistake you're both making is that you're considering only part of the equation. You may eat 2300 calories and only burn 2000, but an additional 500 may pass undigested or unstored as fat. Consequently, you'd effectively be maintaining a 200 calorie deficit (2300-2000-500=-200).
As we all know, some (but not all) carbohydrates are broken down to create glucose. Glucose then yields insulin release(us type 1s being the exception). Insulin leads to energy storage (fat in this case). With a low carb diet, fat storage is much more difficult (less insulin production) which means more dietary fat passes through your body.
As I've mentioned previously, think about how our bodies process fiber. Fiber is a carbohydrate and it does contain energy. However, our bodies are unable to breakdown fiber molecules. Consequently, fiber passes through our bodies as undigested energy. It's for similar reasons why fiber helps people feel full (and keep them regular). The article uses a more extreme example to explain that diesel fuel has calories, yet our bodies would process it much differently than normal food.
This concept also supports my theory that there different causes of insulin resistance (aka T2 diabetes). For some, it may be genetics or other uncontrollable factors. However, it's pretty easy to see how your body could develop a resistance/tolerance to insulin after years of massive carbohydrate consumption/massive insulin releases. On the other hand, a ketogenic diet limits insulin release which limits fat storage and glucose is primarily sourced from glycerol after trilycerides are broken down (although I question if it's a treatment for insulin resistance, or a treatment for hyperglycemia).