[Sesse__]

It's not that simple, though. The only way you can detect frequency is by measuring the amplitude (and then differentiate; except of course in an analog circuit, you don't do that exactly, you have some mechanism that tries to track the carrier wave smoothly instead), so amplitude noise will necessarily also become frequency noise. But generally white AM noise will be pushed upwards in the spectrum after FM demodulation, away from the area where you care. (You can also add a hard limiter, which amplifies this effect; even more noise high up, even less noise further down.)