Final answer:
The statement is false; water primarily moves across cell membranes via passive diffusion known as osmosis, not active transport.
Step-by-step explanation:
The statement "Transport of water molecules occurs through osmosis (simple diffusion), but also occurs through active transport mechanisms, the latter of which allows for faster transport" is false. Water transport across cell membranes chiefly occurs via osmosis, which is the passive diffusion of water from an area of lower solute concentration to an area of higher solute concentration, usually facilitated by aquaporins.
Active transport, on the other hand, moves molecules and ions against their concentration gradient and requires energy. It is not a primary method for the transportation of water molecules.