This paper critically examines the theory proposed by Gabaix et al. (Nature, 2003) that power law tails in price fluctuations arise from volume fluctuations modulated by a square root market impact function. The authors identify three major flaws in the theory. First, they demonstrate that the statistical test used by Gabaix et al. to support a square root market impact—based on the linearity of E[r^2|V]—lacks power in the presence of strong autocorrelations in order flow (signs and volumes). Using real transaction data from the London Stock Exchange (LSE) with an artificially imposed market impact of β=0.3, they show that the test still yields a linear relationship for large numbers of trades, incorrectly suggesting a square root law. Second, they provide new measurements of average market impact at the individual order level for both NYSE and LSE stocks, with proper error bars accounting for long-memory volatility. The results show that the market impact function is not universal: for NYSE stocks it is concave with exponent β<0.2 for large volumes, while for LSE stocks it follows a power law with β≈0.26, both significantly less than 0.5. Third, they find that for LSE stocks traded electronically, the distribution of transaction volumes does not exhibit power law tails, and the return distributions vary substantially across stocks despite similar volume distributions. These findings collectively refute the claim that power law tails in returns are driven by volume fluctuations. The paper concludes that the true origin of large price fluctuations likely lies in liquidity fluctuations and the stochastic properties of order placement, as suggested by subsequent work.