You're actually quite far off about Marx and the State, and are presupposing the Anarchist as the "legitimate" and "original." For Marx, Engels, Lenin, and other non-Anarchist Socialists, the state was the tool of class oppression. The goal of Marx and Engels in their analysis was to show that the centralization of Capitalism leads to public ownership and planning, not decentralization. From Engels:

But to recognize the French Revolution as a class struggle and not simply as one between nobility and bourgeoisie, but between nobility, bourgeoisie, and those without any property, was, in the year 1802, a discovery of the greatest genius. In 1816 he declared that politics was the science of production and foretold the complete absorption of politics by economics.[23] Although the knowledge that economic conditions are the basis of political institutions appears here only in embryo, what is already very plainly expressed is the transition from political rule over men to the administration of things and the guidance of the processes of production -- that is to say, the "abolition of the state", about which there has recently been so much noise.

Further along:

The first act in which the state really comes forward as the representative of the whole of society -- the taking possession of the means of production in the name of society -- is at the same time its last independent act as a state. The interference of the state power in social relations becomes superfluous in one sphere after another, and then dies away of itself. The government of persons is replaced by the administration of things and the direction of the processes of production. The state is not "abolished", it withers away. It is by this that one must evaluate the phrase "a free people's state" with respect both to its temporary agitational justification and to its ultimate scientific inadequacy, and it is by this that we must also evaluate the demand of the so-called anarchists that the state should be abolished overnight.

Anarchists seek abolition of hierarchy, Marxists seek abolition of classes. You can be an Anarchist, but don't distort Marx to suit your ends.