I had this exact same discussion / 3week interrogation by my boss. It went so far as I was required to show a grounding of the neutral connection to the isolation transformer in the inverter despite what was shown in the inverter installation manual. And just like you guys said, the whole discussion is where does the unbalanced current go?
There is no unbalanced current. When the inverter is connected to the grid, the grid is a far bigger current sink than anything local to the inverter, so all the phase outputs of the inverter see the same load.