Sounds very logical, however my personal (anecdotal) experience does not corroborate that.
I went slow carbs kind off accidental. I discovered that eating wheat was the cause of gut problems I had. I stopped (replaced mainly by Spelt, which apparently has a much lower effect on insulin production) and within weeks my clothes were too loose. Now two years later I have the same size in my jeans as I had when I was 18.. (lost about 20 kg)
If you look at the total of carbs I get today, it doesn't differ too much from before. Mostly since I never did eat much processed food or food with white sugar in it. Yet all the 'middle aged' fat is gone.
So while it sounds logical, ' you get the same amount' , the body does not work as a simple math equation. So far the best fitting explanation I've seen is the effect of insulin produced. Not even glycemic index gives you the full picture. Spelt has a high glycemic index. Yet it made the world of difference for me. But from what I've read, it does seem however that you produce less insulin.
I think the biggest mistake made is the idea that you can simply count the calories in food and expect that is all there is to it. We are not petri dishes