Here's the logic: the liquids you brought on board in London are a known quantity, and "safe." Once you've arrived in the states, you had access to your checked luggage while going through customs, and before rechecking it. You could have switched the "safe" liquids for some "evil" liquids that were in your checked luggage before rechecking your bags, and hence be carrying "evil" liquids onto the plane.

IF (and I'm not supporting this if), you believe that having a liter bottle of unknown liquid in carryon luggage on a commercial airliner is enough of a security risk that it should be barred, then the policy goalie describes above actually makes sense.