A fable, such as Animal Farm, usually isn't a direct translation of the situation, on which it is a commentary, into fiction. There is an intermediary step in which the original situation is interpreted, and it is this interpretation which is represented in the tale.
For example, if Animal Farm were a simple retelling of how the rule of Tsar Nicholas II was overthrown by the Bolsheviks etc. using animals instead of humans, there would have to have been a world war, the help of the UK and France during the Russian Civial War, and so on, all of which are missing from Orwell's tale.
Instead, Animal Farm is a retelling of how Orwell understood those events. Orwell has stated that he wrote Animal Farm not to chronicle historic events, but to "expose the Soviet myth". That is, he viewed those historic events in a certain way – that a "violent conspiratorial revolution, led by unconsciously power-hungry people[,] can only lead to a change of masters" – and wrote an allegory of that view.
It is important to note that that view isn't a fact or truth in the same way that the existence of Tsar Nicholas and the revolution of the Bolsheviks are! It is the common Western view on those events. There are of course other possible interpretations of that part of history, and I am sure fables have been written from those views. If you take your understanding of Animal Farm as the reality behind it, you miss how fables work.
The intermediary step of interpreting reality and writing a fable about that interpretation is what makes the fable both internally coherent and, because it is one step removed from reality, "subtle". Reality isn't usually coherent at all, because it is full of parallel, unrelated chains of events, that only coincidentally intersect, as well as random forces, that have no aim or purpose at all.
