You have no right to the loot in a public group. I fully understand your point but it is a sentiment best reserved for FC/LS parties. I can ask to greed MNK stuff to my mates because they know I will pass on anything I don't directly need. In public there is no guarantee you will ever see the rest of your party again thus no basis for such trust to be established. Just farm myth up to get an alt geared while supplementing with pieces from dungeons then run the trials yourself.