Wouldn't this pump water into your cold water supply?

It does use the cold side to circulate the hot water, but there is a comfort valve at the faucet that cuts the hot water flow when you turn on the cold water so there is a only a few seconds of warm water at the cold tap.

This is exactly how the system functions, utilizing your existing cold water line as the recirculation loop to allow a path for the cold water in the hot water line to recirculate back to the hot water heater. However, the thermostatically controlled valve that installs under your farthest sink only allows the water to circulate until hot water reaches the valve. It then shuts off the flow of water until the water at the valve cools, then the process repeats. You may get a very small amount of warm water when you turn on the cold side of your faucet. It's a small price to pay for instant hot water.