Is this correct?

So from what I understand, if I don't eat over my BMR, I'm not supposed to gain weight, correct?

I did the BMR calculator and then multiplied it by 1.2 to find out my maintain calorie intake, which turned out to be 2884. I have calculated my calorie intake for a long time, and on a bad day it reaches 2000. I gain weight on this intake level by an insane amount, due to this I got blood work done to check my thyroid, but the reason i'm asking this is about my original question at the top, I'm having a dispute with a friend who tells me you have to exercise a lot and that i'm eating waaaaay to many calories. I agree that exercise is good for your heart and important for health, but it seems like it mainly just trims off some calories that you ate basically. So am i correct about my original question, or is my friend correct?