Really the correctness of this argument hinges on what definition of inequality one uses. A single factor like standard deviation, for example, tells one much too little. Outliers have a disproportionate effect on this. On the other hand, the gap between what might be called "poor", and "middle-class" affects almost everybody, and the power imbalance that results from this difference leads to many negative effects for those who can't keep up. In summary: the disproportionate influence of the super-rich, and the relative condition of the lower classes are separate issues that are both sloppily discussed using the term "income inequality".
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Really the correctness of this argument hinges on what definition of inequality one uses. A single factor like standard deviation, for example, tells one much too little. Outliers have a disproportionate effect on this. On the other hand, the gap between what might be called "poor", and "middle-class" affects almost everybody, and the power imbalance that results from this difference leads to many negative effects for those who can't keep up. In summary: the disproportionate influence of the super-rich, and the relative condition of the lower classes are separate issues that are both sloppily discussed using the term "income inequality".