Gao et al. (PNAS, 100, 5597-5600 (2003)) have argued that load-bearing mineralized hard tissues. including bones, shells, and teeth, are nanocomposites, in which the mineral phase has nanoscale dimensions that ensure optimum strength and flaw tolerance. In particular, it has been claimed that the thickness of these brittle building blocks, being smaller than a critical size, h*, of the order of tens of nanometers, renders them insensitive to the presence of crack-like flaws and enables them to achieve near-theoretical strength, which is why Nature employs nanoscale features in mineralized biological composites. We find this point of view, which Gao et al. and others have quoted in subsequent publications and presentations, unpersuasive and present several counterexamples which show that biological structures, as a result of being comprised of relatively fragile constituents that fracture at stress levels several orders of magnitude smaller than the theoretical strength, adopt various strategies to develop mechanical responses that enable them to mitigate catastrophic failure. Nanoscale structural features are not a result of an innate resistance to very high stresses.