The change in the transport properties (i.e., water diffusivity, shear viscosity, etc.) when adding salts to water has been used to classify ions as either being chaotropic or kosmotropic, a terminology based on the presumption that this phenomenon arises from respective breakdown or enhancement of the hydrogen-bonding network structure. Recent quasi-elastic neutron scattering measurements of the collective structural relaxation time, τC, in aqueous salt solutions were interpreted as confirming this proposed origin of ion effects on the dynamics of water. However, we find similar changes in τC in the same salt solutions based on molecular dynamics (MD) simulations using a coarse-grained water model in which no hydrogen bonding exists, challenging this conventional interpretation of mobility change resulting from the addition of salts to water. A thorough understanding of specific ion effects should be useful in diverse material manufacturing and biomedical applications, where these effects are prevalent, but poorly understood.