Water molecules can play a striking role in dictating the structure of supramolecular polymer networks in apolar media, but the consequences on their viscoelasticity are not completely understood. Herein, we compare two synthetic supramolecular polymer networks based on hydrogen bonding motifs that coassemble with water molecules in different ways. The first is a biphenyl tetracarboxamide (BPTA) that forms three different helical structures, two of which feature intercalated water molecules. The second is 2,4-bis(2-ethylhexylureido)toluene (EHUT), for which water molecules act as chain stoppers. Networks of each motif in n-dodecane were studied by light scattering, linear viscoelasticity, and passive microrheology while controlling the environmental conditions. At low temperatures in the presence of traces of water, both motifs form networks of dynamic, "living" supramolecular polymers. At high temperatures, in striking contrast to EHUT networks, BPTA networks behave like conventional covalent polymer chains. The counterintuitive behavior of BPTA networks is proposed to originate from enhanced dynamicity enabled by intercalated water molecules at low temperatures.