You are kind of wrong, in that the effect of the extra muscle is pretty minimal. See this video on the topic:

What about muscles? Muscles burn 3 times more calories at rest than fat. This sounds impressive, but tissues like your brain, skin or intestines burn way more. In absolute terms, a more muscular body composition makes a difference for how many calories your body burns, but it’s relatively small. Muscles matter a lot for health, longevity and performance, but not that much for weight loss.

https://www.youtube.com/watch?v=vSSkDos2hzo