I'm not a mechanic, but this doesn't sound right at all. Wouldn't engine RPM and prop RPM be separated by a gear system?
Only in a geared engine. Most aircraft engines that drive propellers are direct drive. The prop RPM and engine RPM are the same. But even in a geared engine the engine has turn faster if you make the prop go faster by diving faster than the propeller governor can handle.
An engine turning draws in fuel. The amount of fuel for each revolution is metered by carburetor or a fuel injection system. The intake stroke of each piston draws in the fuel air mixture. That amount of fuel times the number of cylinders is remarkably unchanging. The ratio of fuel to air is fairly constant. The ideal stoichiometric ratio is 14.7.
What that means is that there is 14.7 times as much air as fuel by MASS. It changes a little for various circumstances but not an incredible amount. A little richer for high power situations to lower the combustion temperature and the risk of detonation and leaner during periods of low demand for fuel economy.
But for most purposes the amount of fuel sucked into a given engine for ONE revolution does not change very much.
What we change is the number of times per minute the engine turns by giving the engine more air. More air means the engine can accelerate to a new RPM level with its attendant increase in fuel consumption over time.
The car example rolling down a hill is analogous to the aircraft. In a car you can separate the engine from the drive train using the clutch. The engine runs at idle RPM, burning X amount of gas per hour. When you engage the clutch then the engine must turn at the RPM of the drive wheels. The throttle is still set to deliver the fuel for idle. Fuel use for each RPM doesn't change but the number of RPM increases so fuel use has to increase when viewed over time.