this is another one of those things that's true in a sort of broad sense, but factually incorrect. exercise burns calories, and burning calories makes you lose fat - that's just basic math.
but exercise makes you hungry, and to the article's main point: people are terrible at estimating calories. a one-hour easy run, a two-hour bike ride, or a full day of alpine skiing burns what's basically an irrelevant amount of calories. if you're taking in any extra amount of calories, normal amounts of exercise doesn't help you lose weight.
It's not just that exercise makes you hungry, it's also that deliberate cardio exercise can lead to you unconsciously moving less throughout the day, therefore reducing your total daily expenditure, in effect cancelling the whole effect of the exercise. E.g. If someone were to run a marathon, especially if they're untrained, they would be too tired to do anything else during that day (I imagine).
You can theoretically try to counter this by also using a step counter to make sure you keep moving throughout the day, but at some point you might be too exhausted for even that to help.
That said, most people don't move or exercise nearly enough, not for weight loss nor for general health, so for most people's situation you're probably right, adding some exercise is a net benefit. It's still much easier and faster (and more important in the long run) to control caloric intake.
but exercise makes you hungry, and to the article's main point: people are terrible at estimating calories. a one-hour easy run, a two-hour bike ride, or a full day of alpine skiing burns what's basically an irrelevant amount of calories. if you're taking in any extra amount of calories, normal amounts of exercise doesn't help you lose weight.