Yes, exactly. Not only the claim of the statement, also the conclusion is wrong. Where did you get it?
We should clarify which kind of "noise" we are talking about. A current loop specifically cancels the effect of common mode voltage differences between transmitter and receiver ground.
Is exctly the contrary. The current loop is less sensitive to environmental noise due to the high impedance of the current generator (ideally infinite). Usually the noise is induced by an electrical field that causes a noise voltage across the wires. Since the high impedance of the generator a very small current can flows in the mesh (is a simple series circuit) that means only a small noise current can be superimposed to the transmitted current. This is even more effective if the receiver resistance (that has to be placed closed to the receiver) is low.