There are a few myths about this and while I hate to gainsay a GP I think she is wrong in this instance. Fat isn't the only thing to turn into fat. Carbs and even proteins can turn into fat. A more accurate way to describe it is that fat is the easiest thing for the body to turn into fat, carbs can also be turned into fat but it takes a bit more energy, and it takes a lot of work for the body to turn protein into fat.
It's hard for the body to break down fat as an energy source. It prefers carbohydrates as fuel. So unless you have a calorie deficit (ie. you've eaten fewer calories than it takes for your body to maintain its weight) your body will turn any fat you eat into fat. It's too much hard work to break it down for energy and the body is an inherently lazy thing.
The best energy source for the body is carbohydrates. The body breaks down the carbs and takes the resulting sugars and puts them into the bloodstream where organs can quickly use it for energy. It also stores some as glycogen in the liver for later energy use. Anything left over is stored as fat. Then the laws of fat apply and the body won't burn that fat unless it has a calorie deficit and needs that fuel.
Protein is used as a building block by the body. It's broken down into peptides and then into amino acids. The amino acids enter the bloodstream where they are used to build and repair muscle and enter the body's protein stores. Excess amino acids are then broken down into fats and sugars, which follow the above process and then can be added to your fat stores unless you have a calorie deficit
and the body needs those fats and sugars to operate.
So all three can become fat, it just takes a hell of a lot more processing to turn protein into fat than it does to turn fat into fat!
This is why, in my opinion, calorie intake vs. calorie output is still the driving force of weight gain and weight loss. If you eat more carbs than your body needs it will turn those carbs into fat. If you eat more protein than your body needs it will turn those amino acids into sugars and fat.
That said, given it actually requires energy (ie. burns calories) to turn protein into fat you would have to eat a lot more over your recommended daily calorie intake for protein to turn to fat than if you were eating mostly carbs or mostly fat. So in that regard the low-carb, high protein diets are right. However if you eat far too much you will still get fat! Another way that low-carb diets work is that fat and protein keep you fuller longer (remembering that most low-carb diets permit more fat than other diets), so while these types of diets claim it's not about calorie counting the main reason they work is because you eat less and as a result consume fewer calories!
The carbs vs. fats vs. protein debate is a highly contested topic in weight loss circles. Many people have a different dog in the fight and will back other viewpoints. I'm on the side of calorie counting, which is usually a pretty unpopular side to be on! I personally believe it all comes down to calories consumed vs. your metabolism of those calories and the processing of different food types is just another element to add to the equation. Others may think differently and I'm happy to listen to their opinions too.
Hope this helps!