No, it is not necessarily true.
A metabolic rate or basal metabolic rate is the amount of energy you expend while you are at rest and your digestive system is no longer active. This normally requires about 12 h of fasting.
Many factors affect BMR. These include:
Here's a link to a BMR calculator that you can use to determine your own BMR.
What determines obesity is not BMR, but the difference between calories needed and calories consumed.
An obese person can have a low BMR and eat a "normal" amount, while another can have a high BMR and eat 5000 Cal/day.
Clinical studies tend to show that most obese people have a high BMR and underestimate the amount of food they eat.
Here is a handy calculator to determine weight gain/loss in terms of calories consumed.
To lose or gain 0.5 kg/week, you will probably have to shave 500 Cal from your daily menu.
If you consume 500 Cal more per day than you burn, you will gain 0.5 kg/week.