Thanks for clarifyingThanks for reading. I wouldn't exactly say that it's counterintuitive (although carnitine is anti-thyroid). Carnitine does increase the total amount of fat burned; which is most likely due to it improving mitochondrial function by restoring glucose oxidation. This then allows for more fatty acid oxidation. So the increase in fat oxidation is due to more and better functioning mitochondria, and not necessarily due to a higher rate of beta-oxidation per mitochondria.
So in other words, carnitine helps to lower excessive pathological fatty acid oxidation, but in the long term (by increasing total mitochondria), it can allow for more "healthy" fat oxidation.
But just because carnitine has a "good" aspect, such as promoting glucose oxidation, doesn't mean it should be used for that reason, because carnitine has its own side effects and there are better and smarter ways to restore glucose oxidation.