He is right in principle, but I don’t know the size of the effect.
Cardiac muscle is somewhat famously metabolically flexible, in that it can derive energy from fatty acids and central metabolites without any real lag time in expressing enzymes. Contrast that to most tissues, which tend to be best at oxidizing one substrate and take some time to adapt to another. This is the reason for the “carb flu” when going into ketosis… the body is all geared up to burn blood sugar, but even when ketone bodies are everywhere, it takes some time to express the enzymatic machinery to use them efficiently. Because the heart (and some parts of the brain) can’t really slack off, they operate a bit differently — they seem to prefer fatty acids, but can swap over to carbohydrate immediately.
The idea with beta blockers and clen is fairly simple. Cardiac tissue can chew through fatty acids, and if it’s going faster it will consume more. By reducing heart rate (and BP, to a degree), the heart does less work and so burns fewer calories from free fatty acids.
The question is how large that effect is. I would be surprised if it was as much as 10 additional kcal/hour.