True enough if comparing to something such as 20 reps, which won't do much to raise your metabolism. I thought you were referring to the really heavy stuff where you do a couple or three reps, go for a cup of tea and come back to do a different exercise, ie "powerlifting".
That's seriously intense but simply doesn't have time to burn many calories. Somewhat simplified but calories are literally burnt, meaning oxygen, meaning aerobic rather than anaerobic. I know it's splitting hairs but very low rep stuff just doesn't burn many calories, intense or not. Running out of steam for the 6th rep doesn't mean you've burnt all your body's energy reserves via either aerobic or anything else, just that you've fatigued enough fibers that you can't lift that weight anymore - and most of that is from neural motor units, not glycogen reserves or anything.
Heavier weights will recruit more fibers but not twice as many, yet with high reps you can easily be doing twice the reps, even triple. If you look at a graph you can easily see a big difference in volume for example. Take 6 reps at 50lb, for whatever exercise, that's only 300lb total. Make it 3 sets, 900lb.
Now do 14 reps at 30lb - that's 420lb per set, 1260lb for that exercise. Simple physics sez 1260lb requires more calories and is more work than 900lb.
When you increase the weight not only the reps but the overall volume goes down, as muscles don't behave perfectly linear - your 12RM isn't
half of your 6RM, its more like 3/4 of it (I can check and be precise if you like but you get the idea!).
What was the question again?