The comment offered by this novel certainly relates to the nature of power, but extending that commentary to a message regarding human nature may be going a step too far. The characters in the story all represent "people" and there is clearly an array of traits and tendencies presented in the characters on the farm.
To draw just one example, Boxer is quite different in temperament, ability, and intellect in comparison with Snowball. Drawing a conclusion regarding human nature then will be quite difficult due to the complex and manifold differences in the characters.
There is, however, a definite commentary made on power and powerlessness, corruption and the nature of political bodies.
Snowball and Napoleon, as leaders, both allow themselves to be corrupted and carried away by the sway of their own power. Squealer is their mouthpiece, articulating arguments that excuse the special privileges given to the pigs.
First, they alone are allowed to consume the milk and the apples which Squealer claims they do not really want to take, but must to preserve their strength.
From milk and apples, the pigs move on to living in the farmer's house, completely upsetting the balance of equality and eventually abusing their power.
Before they had power, the pigs were not evil or corrupt. After they realize what they can get away with, power becomes intoxicating for the pigs and they fall into abusive behavior.
Orwell knew that with power came the abuse of power and only a vigilant citizenry could prevent such abuses.