We present a systematic analysis of the accuracy of a series of SCANα functionals for water, with varying fractions (α) of exact exchange, which are constructed through the adiabatic connection formula. Our results indicate that that all SCANα functionals exhibit substantial errors in the representation of the water 2-body energies. Importantly, the inclusion of exact exchange is found to have opposite effects on the ability of the SCANα functionals to describe the interaction energies of water clusters with 2-dimensional and 3-dimensional hydrogen-bonding arrangements. These errors are found to directly affect the ability of the SCANα functionals to describe the structure of liquid water at ambient conditions, which is investigated using explicit many-body models (MB-SCANα) derived from the corresponding SCANα data. In particular, it is found that all MB-SCANα models predict a more compact first hydration shell, which results in a denser liquid with a more ice-like structure. These ap- parent opposite trends can be explained by the inability of all SCANα functionals to provide a balanced description of the water 2B and 3B energies at the fundamental level. The analyses presented in this study provide new insights that can guide future developments of improved exchange-correlation functionals for water.