NO NO NO NO NO. Greenboard is moisture resistant only. Not waterproof. It will fall apart and does support mold growth.
Hardibacker or Durrock are fine for what you are doing. It should be attached to the floor with thinset adhesive and screws. Seam the joints with fiberglass tape and skim with the thinset. Keep the rough side up. When setting your tile use the good thinset, the one with the additives. White for light tile, Gray for dark tile.
Don't forget a vapor retarder. You should appply it to the studs before you put up the backerboard. Tyvek is tough and works well, you can also use Aquabar or stucco paper, but they can tear fairly easily. Some brands recommend a poly sheeting, but that can cause condensation. You want to allow for a little vapor transmission that's why I like Tyvek.
I have done 3 out of the 4 bathrooms in my past 2 houses over the last 25 years and have never had a problem using greenboard. Besides, in a shower, you normally tile to above the shower head and hot mop any areas that water will come in contact with on a daily basis. Again, not trying to say you guys aren't right about it, but just my 2 cents about the greenboard