We present terahertz (THz) measurements of salt solutions that shed new light on the controversy over whether salts act as kosmotropes (structure makers) or chaotropes (structure breakers), which enhance or reduce the solvent order, respectively. We have carried out precise measurements of the concentration-dependent THz absorption coefficient of 15 solvated alkali halide salts around 85 cm(-1) (2.5 THz). In addition, we recorded overview spectra between 30 and 300 cm(-1) using a THz Fourier transform spectrometer for six alkali halides. For all solutions we found a linear increase of THz absorption compared to pure water (THz excess) with increasing solute concentration. These results suggest that the ions may be treated as simple defects in an H-bond network. They therefore cannot be characterized as either kosmotropes or chaotropes. Below 200 cm(-1), the observed THz excess of all salts can be described by a linear superposition of the water absorption and an additional absorption that is attributed to a rattling motion of the ions within the water network. By providing a comprehensive set of data for different salt solutions, we find that the solutions can all be very well described by a model that includes damped harmonic oscillations of the anions and cations within the water network. We find this model predicts the main features of THz spectra for a variety of salt solutions. The assumption of the existence of these ion rattling motions on sub-picosecond time scales is supported by THz Fourier transform spectroscopy of six alkali halides. Above 200 cm(-1) the excess is interpreted in terms of a change in the wing of the water network librational mode. Accompanying molecular dynamics simulations using the TIP3P water model support our conclusion and show that the fast sub-picosecond motions of the ions and their surroundings are almost decoupled. These findings provide a complete description of the solute-induced changes in the THz solvation dynamics for the investigated salts. Our results show that THz spectroscopy is a powerful experimental tool to establish a new view on the contributions of anions and cations to the structuring of water.