The genomes for all three viruses have been published so it's easy enough to find the differences. But that doesn't directly tell us why the fatality rates are different.
I don’t really understand why this is a “rule.” Say there’s two viruses and it takes both 3 weeks to run their course. They are both equally contagious during the 3 weeks, however the first virus results in death for 50% of those infected (50% recover after 3 weeks and are no longer contagious), and in the second the death rate is only 1% (99% recover after 3 weeks). Is such a virus not possible to exist?
the rule being discussed doesnt apply to a virus that reproduces and transmits to another host before causing illness.
the basis of the lethality and transmissibility are inversely related is dependent upon dead or ill hosts having down time and not interacting with other hosts. thus if you are sick and febrile, you contact fewer individuals thus less opportunity for virus transmission between individuals.
in the case of the coronavirus the dynamic is different.
you contact the virus, virus replicates, and becomes transmissible, you still feel fine and behave as always transmitting the virus to other individuals, Then you begin to feel ill and bedridden. the virus has reproduced, transmitted and even if it kills you, it has escaped the selection pressure of the first case, where lethality or morbidity must be decreased for maximization of transmission.
here is a slightly difficult read but is is a classic example of the rule you are asking about.