Sorption of water vapor in cellulosic materials has been studied for more than 100 years. However, the last 2 decades have seen a surge in studies of sorption kinetics due to the adoption of automated sorption balances in laboratories worldwide. Sorption kinetic data is commonly fitted with the parallel exponential kinetics (PEK) model, which is the sum of two exponential functions. The PEK model parameters are often interpreted as representing physical quantities or material properties, but their exact definition remains undetermined. Nonetheless, PEK fitting of sorption data has been widely used to identify various physical properties. Recent work has called into question the protocols used to collect sorption data with automated sorption balances and the methods used to analyze the data. Typically, data acquisition is interrupted before equilibrium when the rate of mass change fulfills a user-specified criterion, and this has been shown to severely mischaracterize both the equilibrium moisture content and the full kinetic behavior. The objective of this work is to examine whether interrupting data acquisition before equilibrium affects the PEK model parameters and further explore whether PEK model interpretations have physical significance as claimed in the literature. The analysis shows that the PEK model cannot capture the actual form of the sorption curves for loblolly pine and microcrystalline cellulose across a range of relative humidity (RH) steps in both absorption and desorption. PEK model parameters depend not only on the mass stability criterion that controls the measurement hold time, but also on the RH step making even qualitative comparisons of a single sample across different RH steps meaningless. The PEK model cannot be used to derive physically meaningful properties from water vapor sorption measurements and its use as a tool for exploring the properties of cellulosic materials interacting with water is not recommended.