What I don't see is how it explains why one would work better than the other.
If the tree is blowing in the wind, and a leaf obstructs the entire signal, it doesn't matter whether it's a change in brightness, or a change in color. Either way, that information is lost by the blocked leaf. And if the entire signal is not lost, perhaps many leaves may have blocked the signal but some signal managed to get through, it doesn't matter whether the signal change was a change in brightness, or a change in color. Either way you're going to notice the change. So I don't see how this clarifies why FM is better. What am I missing?
I see from the article that "noise tends to be a an unwanted amplitude modulation, not a frequency modulation." In other words, the tree is providing an unwanted change in brightness. It never provides an unwanted change in color.
I guess the tree is able to dim the signal so much that it appears to be a deliberate signal change? Couldn't this be dealt with if you know the details of the tree's dimming ability?
I'm unsure of what the correct terminology would be, but (for my linear algebra brain) you could say something like, for FM the noise dimension is orthogonal to the signal dimension, while for AM the noise and signal dimensions are the same. Therefore for FM any change in amplitude in the noise dimension should be mostly isolated from the signal dimension, while it is essentially impossible to tell what is noise and what is signal for AM - you could probably do some radio equivalent of a differential pair in order to detect noise and remove it, but then why would you bother when FM has improved noise rejection anyway.
Ps I don't think analogies are helpful.
The claim 'the effect of random noise is to amplitude modulate' is probably not 100% correct, because to my understanding it's not actually performing modulation (the modulation happens at the transmitter but the noise happens between the transmitter and receiver), but it is impacting the amplitude at a given frequency and to a receiver this is impossible to know whether said change in amplitude happened before modulation (signal) or after modulation (noise).