Taken from a handbook of mine - "The communications effectiveness (of FM) depends almost entirely on the receiving methods. If the receiver will respond to frequency changes but is insensitive to amplitude changes it will discriminate against most forms of noise ..."
My understanding, which may be oversimplified, is that in some FM receivers a bunch of the incoming signal has the top chopped off - where the amplitude is varying - because it doesn't need that - it only needs to see the variation in frequency. In AM you need the variations in amplitude because that is where the information is contained.