Sorry highlife, not so.
The engine is more efficient at altitude (same power, less fuel flow) because the operating temperature of the engine must be higher at altitude to produce the same power. Power is produced by making a given package of air rise a given amount of temperature (which makes it have higher pressure) then blowing that package of air against a turbine wheel to extract the power. At altitude, the package of air is less dense, so the temperature it must be raised to is higher for the same power.
The temperature difference between the air package and the environment determines the thermodynamic efficiency of the process. Ideally, one air molecule, heated to 1,000,000,000,000 degrees could produce enough power to hover. But since that molecule would melt its way through any turbine we can build, we are stuck with raising a few pounds of air to about 900 degrees C, and then extracting the energy.
To recap, efficiency of an engine is determined by the temperature difference between the turbine inlet and the outside air. More temp, less fuel burned for a given power. The quest for lighter, more efficient and more powerful engines has been the quest for better turbine metals that aloow higher temperatures.
This is also the reason why twins burn more fuel than singles to do the same job, and three engined helos more fuel yet. It is also why a helo with two big engines that allows OEI hover on one engine will burn more fuel than a twin with two small engines.