You are incorrect. The above is only true in the special case where the loads have current waveforms that cancel, such as resistive loads, matched inductive loads, or power-factor-corrected power supplies as loads (often found in servers). The above claim is *NOT TRUE* for cheap switching power supplies sharing a neutral. In that case each phase has a huge current spike at the peak of the voltage waveform (think capacitor being kept charged through a bridge rectifier).
I strongly recommend that you read section 7 ("Why do 3rd harmonic currents overload neutral conductors") of the following FAQ: [
There are harmonic standards (USA IEEE Standard 519-1992, EU Standard EN61000-3-2) that attempt to put the burden of keeping these harmonic currents at a safe level on equipment manufacturers, but the person who buys a couple of hundred cheap personal computers and installs them in an old buildings to replace electric typewriters often doesn't know anything about this and ends up overheating the neutral.
Also see:
[-- ( G o o g l e F o o d . . . )