There are 3 options when rolling for an item. Need, Greed and Pass. If you chooses Need for the item any Greed rolls are infereior than yours. Its the exemple you descibred at post #1, the guys who won the item with a 2 roll selected Need for it, the other guy who rolled Greed with a roll of 45. He could had rolled 100 and he would still looses for the Need.

The Need option is available if you can wear the item. Ex: Mind item drops and you beeing a healer, the Need option will be available to you. As for the tank and the other DPSs, only Greed and Pass options will be selectable.