agree with your statement and will add that after a few weeks of the reduction by 500 calories, you can up it to a 1000 calorie reduction. as long as it's done safe and smartly (as in you don't literally change it by 500 additional calories in one day, instead gradually and continue to intake vital proteins, healthy carbs and fats during that time) you shouldn't have a problem.
1 pound = 3500 calories.
it is more realistic to aim for 1 lb/ week, not 2.
then to lose 1 lb/wk, eat 500 calories less per day than you eat.
that 500 calorie loss per day can come from eating less, exercize, or a combination of both.