This is just my opinion and with no specific code reference. I believe your forman and Roger are correct in that a neutral is not required for a sub-panel. If the pool subpanel is originally designed for 240 volt loads only and it is filled to capacity with 2-pole breakers then obviously there is no need for a neutral. However, Larry also brings up a good point about 120 volt loads. Even if the pool panel didn't require any 120 volt loads at the time of installation, if it is left with the capacity for more breakers there may be a situation, at some point in time, to run additional circuits that are 120 volt (i.e pool lights, landscape lights, etc.). If you were the original installer and didn't pull the neutral in you basically stuck the next guy.
Just my 2 cents worth.