I'm sorry to tell you, but it's not true. Calories do count on Shabbat.
The problem is that you have no way to count them. If you belong to Weight Watchers or another strict weight-loss system, then you had better be eating your own food at home, with each meal planned ahead of time. You have no idea how your host has fixed those dishes or even what all is inside them. The best you can do is watch your portions, eat the most un-processed fruits and vegetables you can find, and avoid any particular foods prohibited by your diet (such as carbs or meat).
If you have any advice about keeping track of your food intake on Shabbat, feel free to share it below. While I likely won't benefit from the advice (I follow what I said above), I know this is a subject that a lot of people would like to discuss!