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Is the exponent 3/2 justified in analysis of loading curve of pyramidal nanoindentations?

Kaupp and Naimi-Jamal (2010) claimed that the analysis of published loading curves reveals the exponent 3/2 to the depth for nanoindentations with sharp pyramidal or conical tips. To demonstrate this, they plotted the load vs. the penetration depth to the power 3/2. We show, through examples, the authors' assertion is not credible because the methodology used is misleading and it cannot be asserted that the exponent 3/2 has a universal validity that applies to all kinds of materials.