I cannot see elite operations as being either Neutral or Independant when they employ omni thugs. Indirectly you are funding a side in this war by paying soldiers of the Omni Tek corporation.
When there are two sides to a conflict, having an affilation with either one immediatley stops you from being Independant. You have chosen a side, and it seems to me that it is Omni Tek who have hired the thugs.