Hi Maria.
Chomsky makes many of the mistakes that I mention in my article. His view of power is too limited, focusing on governmental power as the source of injustice. Granted, he does acknowledge corporate power, which leaves him one up on most of those who are sympathetic to anarchism.
His main problem is that he sees the power relation between government and people as necessary antagonistic. Your assessment of his stance as the need for the power to overthrow government is fair, but that principle is not anarchism, it goes back to John Locke. Remember that Locke's position is that we replace a tyrannical government with a representative government. Anarchism is the demand for no government. Very different.
No, it is not the task for government to prove their legitimacy. The burden of that task can't be placed on any one element of society. To demand that government prove itself is an abrogation of one's own responsibility in determining the legitimacy of power structures, which I remind are far more than government. The issue remains that anarchists a priori reject any possibility for legitimate authority, removing themselves from the necessary conversation about social power relations.