Is this an exam statement (like a trick question or true/not true selection), because that's simply not true.
Consider this simplistic example: a Mealy machine with two states "Quiet" and "Talk" and an extra input signal "Message". The machine could be constructed such that when the machine is in the "Quiet" state, its output might remain at 0. And when in the "Talk" state, the output might be a copy of the "Message" input, allowing the message to be transmitted through the machine.
PS. The advantage of a Mealy machine over a Moore machine is that in the Moore machine, the outputs can only be dependant of the state, whereas in a Mealy machine, the outputs can be dependant of the state and the input(s). So the outputs of a Mealy machine can change whenever the inputs change, even if there is no change in state.