The question is asked: if the government were to recede wouldn't some other organization promptly take over? In earlier incarnations of this fallacy the "other organization" discussed was often the Mafia or other organized crime syndicates. It has since been updated to discuss "the corporations" taking over, and sometimes even specific corporations such as Blackwater / Xe. Since the argument started by using the Mafia, and that is the version closest to having a sensible basis to argue from, the fallacy should be named in honor of the Mafia.
With regards to corporations it is actually an absurd question. First of all, corporations as they exist today exist because of government charter. Without the government, corporations as we know them would not exist. Blackwater is even more special because it would not exist unless the government is itself imperial, as a company like Blackwater would not exist without government as a customer. It is, essentially, an adjunct of government. The powers that corporations have that are abused are powers that were granted by the government.
Corporations, with the power not abused, are there to conduct peaceful voluntary transactions with willing customers. How could they "take over" with that sort of mindset? And what exactly are the critics thinking of when they make that claim? With corporations form police forces and require people to purchase their goods?
That is why the original claim, about organized crime syndicates such as the Mafia, makes a better argument. The classic "protection money" correlates very well to paying taxes. But an analysis of organized crime reveals some flaws even in this.
The primary revenue source of organized crime is engaging in black market activities, the sale of goods or services that are illegal In the 1920s that included alcohol. When alcohol was no longer banned open competition drove organized crime out of that market. When alcohol was banned, competition took place in the form of territorial jurisdiction, while legal goods compete in terms of price and quality.
In the event of a government drawback the primary revenue source of organized crime will disappear. The primary criminal black markets - drugs, gambling, sex - will not have government restrictions. That leaves only the classic activity of protection money as a potential activity for organized crime.
Shakedowns, protection money, unauthorized taxation, that is the point which shows that the fallacy can only work when someone is ready and willing to use coercive force, and why criminal organizations may do this and why discussing corporations makes a much weaker fallacy.
The reason that organized crime is able to do shakedowns is because of their subversion of the police, how officers will look the other way at criminal activity. An individual who attempts to fight back against organized crime will find no help from the agencies that are supposed to assist.
But it has a very small economic return. Government is inherently an unprofitable activity. The shakedowns, under current criminal activities, augment the income of the crime syndicates and are not a major source of revenue. Depriving organized crime of black market revenue while allowing people to defend themselves from shakedown enforcers will make even the Mafia have a hard time instituting a new government.
It isn't impossible, but it is far more difficult than is assumed by those committing the fallacy, and it is only possible for criminal gangs and not the corporations. Not even Blackwater.