Having heard this argument before, and having spent some time thinking about it, I've come up with an additional objection. I'm sure someone somewhere has said this before, but since I've never heard it anywhere it should be worth saying.
Anyone who has read Economics in One Lesson should be familiar with The Lesson:
The art of economics consists in looking not merely at the immediate but at the longer effects of any act or policy; it consists in tracing the consequences of that policy not merely for one group but for all groups.My objection to attributing the comparative wealth of the richest members of society to general government services is based on this methodology. If you are only considering the wealthy, and you find that a lot of them have made use of government programs such as "free" K-12 education, it might seem tempting to attribute a significant amount of their overall success to that service. When you consider the whole picture, however, such a claim begins to seem ridiculous. If a wealthy person became wealthy because of stuff the government gives to everyone, why isn't everyone wealthy? If we seek to explain the differences between the rich and the poor, clearly we cannot rely on conditions that apply to both.
The belief that government services are responsible for conspicuous wealth also suggests a rather cynical view of the poor. If all it takes to become a millionaire is something that everyone gets, what kind of judgement can we make of people who squander this resource? There is no way to escape the conclusion that different outcomes have different causes, so if wealth isn't the result of extraordinarily good effort by the wealthy, then poverty must be the result of extraordinarily bad effort by the poor.
Or maybe the reasoning is fallacious to begin with.